# Math 4 SN Systems Word Problems Practice

Size: px
Start display at page:

Transcription

1 Math 4 SN Systems Word Problems Practice Name : 1 For each week that he works, Fred is paid a fixed hourly wage plus a bonus based on the amount of profit the company makes. Last week, Fred worked 14 hours and received a bonus of \$ This week, he worked 15 hours but his bonus was only \$7.50. Fred said that he earned the same amount of income for each of the two weeks. Next week, how much will Fred earn if his boss guarantees him a bonus of \$30.00 and 20 hours of work? 2 To pay for their team s travel expenses, the members of a football team buy caps and sweatshirts from a supplier and resell them for a profit. The following table shows the number of items sold and the profit made by each of three team members. Number of Number of Profit Caps Sold Sweatshirts Sold Eddie 8 20 \$162 Gary \$148 Jonathan 6? \$167 How many sweatshirts did Jonathan sell? 3 Nancy has hired a caterer to prepare a dinner to celebrate her grandparents' wedding anniversary. The following are two bills for meals prepared by this caterer. Bill Bill Meals for Meals for 15 adults 10 adults 5 children 1 child Total \$315 Total \$189 Nancy asks this caterer to prepare the same type of meal for 51 adults and 9 children. What will be the total cost of the food for this dinner party?

2 4 A chemist wants to find out what chemical elements are used to make up a mixture. He knows that the mixture is made up of 2 of the following four elements.. Element Atomic mass (g) Aluminum Calcium Chromium Copper x and y represent the atomic masses of the unknown elements The relationship between the sum and the difference of the atomic masses of the two unknown elements is given by 3x + 4y = 289 and 3y 5x = 21. What elements make up the mixture? 5 6 A school organizes a lottery to enable it to buy a computer. If each ticket sells for \$2, the school will be short \$1000. However,if they sell each ticket for \$3, the school will make a profit of \$250. How many tickets does the school need to print and what is the price of the computer? At an amusement park, there is an entry fee and a charge for each ride on the merry-go-round. Three friends went to the park. Susan spent a total of \$10.50 for the entry and 10 trips on the merrygo-round. Maria spent \$13.50 to enter and take 14 rides on the merry-go-round. How much did Sophie have to pay for the entry fee and 8 rides on the merry-go-round? 7 Marcel took his family to a concert and paid \$21.50 for 2 adult tickets and 5 children's tickets. He also paid \$132 for 16 adult and 24 children's tickets for the members of his social club. What is the value of the 2 adult tickets and 1 child's ticket which were used by the Smith family who are members of the club? 8 A businessman made two long distance phone calls from his office to the same place. This is the bill he received for the calls: Length of the phone call Cost (in minutes) \$7.80 \$12.00 The cost of a call is made up of a basic fixed charge for the first minute followed by a fixed rate for each minute after that. How much would a 2-minute phone call cost to the same place?

3 9 In a particular neighbourhood, 3600 homes were robbed last year. A study showed that 4 times as many of these thefts were committed at night as during the daytime. How many of these thefts were committed during the daytime? 10 Last Friday, 1200 people used the automatic teller at a bank in their neighbourhood. There were 5 times as many people who made a withdrawal as those who made a deposit. How many people made a deposit? 11 A car rental company sets its prices on the basis of a fixed daily rate plus a certain amount per kilometre travelled. Two people rented cars. The first person travelled 300 km and it cost her \$105. The second person went 240 km and it cost her \$96. What is the fixed daily rate charged by the company? 12 In an automobile factory, the personnel department analyzed the causes of absenteeism among its employees. The situation is described by the following system of equations : x = 240 y x = 4y + 40 where x represents the number of absences due to illness and y represents the number of absences for personal reasons. How many absences due to illness were recorded? 13 This year a gardener bought 3050 flower bulbs - tulips and lilies. Because of increased demand, he decided to order twice as many lilies and three times as many tulips for next year. This will bring the total number of bulbs to How many tulip bulbs will he order for next year?

4 14 A local high school ordered 20 balls for basketball and soccer for a total cost of \$825. The price of a basketball is \$40 and a soccer ball is \$45. How many soccer balls did they buy? 15 Edith bought some small tiles and some large tiles to recover a floor. She laid a total of 272 tiles. The design required 2.4 times as many large tiles as small ones. At the end of the job, 40 small tiles and 16 large tiles were left over. How many large tiles had she brought? 16 On the Jean-Lesage highway that joins Montreal to Quebec there is always a lot of traffic. One day last June, vehicles were counted. The cars outnumbered the trucks by 16 to 1. Calculate the number of cars that were in circulation on the Jean-Lesage highway on that day. 17 For home repairs, a technician charges a fixed price plus a certain amount per hour of work. Therefore, it costs \$145 for 3 hours of work and \$100 for 1.5 hours of work. How much would it cost for repairs that require 5 hours of work? 18 In a supermarket, a mix of 0.5 kg of peanuts and 0.75 kg of cashews costs \$ Likewise, a mix of 1 kg of peanuts and 1.25 kg of cashews costs \$ According to this information, how much would a mix of 3.5 kg of peanuts and 2 kg of cashews cost? 19 To go to a rock concert with her friends, Joyce paid \$214 for 4 balcony tickets and 3 main-floor tickets. To go to the same concert, Eric paid \$208 for 5 balcony tickets and 2 main-floor tickets. To go to this concert, how much will Kim pay for 2 main-floor tickets? 20 The length of a rectangle is 8 cm more than its width. Its perimeter is 240 cm. What is the area of this rectangle?

5 1 Answers Let and x : hourly wage y : weekly salary System of equations representing the situation y = 14x + 15 y = 15x Solving the system of equations 14x + 15 = 15x x = 7.50 Income for 20 hours of work and \$30.00 bonus y = = 180 Final answer Next week, Fred s income will be \$ System of equations representing the situation x: profit per cap sold y: profit per sweatshirt sold 8x + 20y 11x + 16y = 162 = 148 Solving the system of equations ( x) + 11( 20y) = ( ) ( x) + 8( 16y) = 8( 148) Since 88x + 220y = x + 128y = y = 598 y = 6.5 y = 6.5 8x + 20( 6.5) = 162 8x = 162 8x = 32 x = 4 Number of sweatshirts Jonathan sold Profit for the caps Jonathan sold: 6 \$4 = \$24 Profit for the sweatshirts Jonathan sold: \$167 \$24 = \$143 Number of sweatshirts Jonathan sold: \$143 \$6.50 = 22 Answer: Jonathan sold 22 sweatshirts.

6 3 x: the cost of a meal for an adult, in \$ y: the cost of a meal for a child, in \$ System of equations 15x + 5y = x + y = 189 Solving the system 15x + 5y = (10x + y = 189) 15x + 5y = x + 5y = x = -630 x = 18 If x = 18 then y = y = 189 y = 9 Total cost of the food for the dinner party 51 meals for adults at \$18 per meal: \$918 9 meals for children at \$9 per meal: \$81 Total cost \$918 + \$81 = \$999 Answer: The total cost of the food for this dinner party is \$ To find the unknown elements, we must solve the system of equations by reduction. 3x + 4y = 289 (1) -5x + 3y = 21 (2) By multiplying equations (1) and (2) by 3, and by 4 respectively, we get an equivalent system. 9x + 12y = x + 12y = 84 Subtract these 2 equations. _ 9x + 12y = x + 12y = 84 29x = 783 x = 27 The first unknown element has an atomic mass of 27 grams. It must be aluminum. Since x = 27, then 3x + 4y = 289 becomes 3(27) + 4y = y = 289 4y = 208 y = 52 The second element has an atomic mass of 52 grams. It must be chromium. Result : The unknown elements are aluminum and chromium.

7 5 Given x, the number of tickets y, the price of the computer System of equations 2x = y x = y Solution of the system of equations x = 1250 and y = 3500 Result : The school has to print 1250 tickets and the computer costs \$ System of equations x : entry fee y : cost of a ride on the merry-go-round x + 10y = x + 14y = Solution of the system of equations x = \$3.00 y = \$0.75 Determining the cost of entry and 8 rides on the merry-goround C : total cost C = x + 8y = = 9.00 C = 9.00 Result : \$ Given x : the price of a child's ticket y : the price of an adult's ticket 5x + 2y = x + 16y = 132 Solving the system of equations 5x + 2y = The values of each type of ticket can be found. 8x + 4y = 33 Use the method of reduction. 2(5x + 2y = 21,50) <---> 10x + 4y = 43 6x + 4y = 33 6x + 4y = 33 4x = 10 x = 2.50 If x = 2.50, then 5x + 2y = becomes 5(2.50) + 2y = y = y = 9 y = 4,50 therefore 2(4.50) = \$11.50

8 8 Translate this situation using the following system of equations: (1) 7.80 = x + 14y (2) = x + 24y where x represents the charge for the 1 st minute and y represents the amount charged per minute thereafter. Solve the system by reduction. (2) = x + 24y -(1) 7.80 = x + 14y 4.20 = y 4.20 = 10y 4.20 y = 10 y = 0.42 (charge for each extra minute) Substitute the value of y (y = 0.42) into equation (1) 7.80 = x + 14(0.42) 7.80 = x = x (charge for the first minute) Cost for a 2-minute call: \$ \$0.42 = \$ Given x = the number of daytime thefts and y = the number of nighttime thefts. Since there were 3600 thefts in all, x + y = 3600 Since there were 4 times as many nighttime thefts as daytime thefts y = 4x or 4x y = 0 The following system of equations represents this situation x + y = x y = 0 Solve the system by reduction. 1) x + y = ) 4x y = 0 5x = 3600 therefore : x = = 720 There were 720 daytime thefts. Result : 720 thefts

9 10 Given x = number of people who made a deposit y = number of people who made a withdrawal "1200 people used the automatic teller..." can be translated by x + y = 1200 "5 times as many people who made a withdrawal as those who made a deposit" can be translated by 5x = y Substitute 5x for y in the equation x + y = This gives x + 5x = 1200; 6x = 1200 and x = 200 Result : 200 people made a deposit. 11 Given x : fixed daily rate y : additional amount per kilometre travelled. The first person travelled 300 km and it cost her \$ = x + 300y The second person went 240 km and it cost her \$ = x + 240y Solve this system to find the fixed daily rate (x) charged by the car rental company. 105 = x + 300y is an equation equivalent to y = x 96 = x + 240y is an equation equivalent to y = x By the method of comparison: x = y = y = x therefore y = y 9 = 60y 9 and y = = If y = 0.15 then x = (0.15) = \$60 = the fixed daily rate. Result : The fixed daily rate is \$60.

10 12 Solve the given system of equations by comparison. x = 240 y = 4y + 40 = x 240 y = 4y y = 200 y = 40 If y = 40, x = 240 y = = 200 Result : 200 absences due to illness. 13 Given x : number of lily bulbs bought this year. y : number of tulip bulbs bought this year flower bulbs : x + y = 3050 twice as many lily bulbs and three times as many tulip bulbs for a total of 7950 flower bulbs : 2x + 3y = 7950 Solve the system of equations by substitution. x + y = 3050 or x = 3050 y Replace x by (3050 y) in 2x + 3y = (3050 y) + 3y = y + 3y = y = This year the gardener bought 1850 tulip bulbs. Next year he wants to buy three times as many. That is, = 5550 bulbs. 14 Given p : the number of basketballs s : the number of soccer balls Purchase of 20 balls in all p + s = 20 or p = 20 s Cost of the 20 balls = \$825 40p + 45s = 825 Since p = 20 s, replace p in 40p + 45s = 825 by (20 s) 40p + 45s = 825 becomes 40(20 s) + 45s = s + 45s = s = 825 5s = 25 s = 5 Result : 5 soccer balls.

11 15 Given x, the number of large tiles used y, the number of small tiles used The system of equations : x + y = 272 x = 2.4y Solution of the system of equations x = 192 and y = 80 The total number of large tiles bought = 208 Result : She had bought 208 large tiles. 16 Let x : the number of cars y : the number of trucks System of equations x + y = x = 16y Solution : by substitution (or another method) x + y = y + y = y = y = 1600 (number of trucks) Number of cars x = 16y x = x = Result : The number of cars that circulated on the Jean-Lesage highway is Equation that defines the situation C : cost of the repairs f : fixed price x : amount per hour of work h : number of hours of work C = hx + f Solving the system of equations 145 = 3x + f 100 = 1.5x + f f = 55 and x = 30 Cost of repairs requiring 5 hours of work C = C = 205 Result : The repairs would cost \$205.

12 18 x : price of 1 kg of peanuts y : price of 1 kg of cashews 0.5x y = x y = By solving the system, x = 5 and y = 11. Therefore, 1 kg of peanuts costs \$5 and 1 kg of cashews costs \$11. Price of the new mix (3.5 5) + (2 11) = \$39.50 Result : The price of the new mix is \$ Given x : price of one balcony ticket y : price of one main-floor ticket System of equations representing this situation 4x + 3y = 214 5x + 2y = 208 Solution of the system of equations x = 28 y = 34 Price of Kim's tickets 2 34 = 68 Result : Kim will pay \$68 for 2 main-floor tickets. 20 Given x : length of the rectangle y : width of the rectangle System of equations representing the situation x y = 8 2x + 2y = 240 Solution of the system of equations x = 64 y = 56 Area of the rectangle = Result : The area of the rectangle is 3584 cm 2.

### Unit Test Linear equations and Inequalities

Unit Test Linear equations and Inequalities Name: Date: Directions: Select the best answer for the following questions. (2 points each) 7L 1. The steps for solving are: 1) Read the problem and label variables,

### Section 2.2 Objectives

Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational

### ALGEBRA I END-of-COURSE PRACTICE

1. Which graph is the solution to the inequality A. 2 x 6 B. C. D. 2. Which of the following tables does not represent a functional relationship? Division of Mathematics, Science, and Advanced Academic

### Name Class Date. Simplifying Algebraic Expressions Going Deeper. Combining Expressions

Name Class Date 1-5 1 Simplifying Algebraic Expressions Going Deeper Essential question: How do you add, subtract, factor, and multiply algebraic expressions? CC.7.EE.1 EXPLORE Combining Expressions video

### Algebra I Practice Exam

Algebra I This practice assessment represents selected TEKS student expectations for each reporting category. These questions do not represent all the student expectations eligible for assessment. Copyright

### Name: Class: Date: ID: A

Name: Class: Date: 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Multiple Choice Identify the choice

### Algebra 1 PAP Fall Exam Review

Name: Pd: 2016-2017 Algebra 1 PAP Fall Exam Review 1. A collection of nickels and quarters has a value of \$7.30. The value of the quarters is \$0.80 less than triple the value of the nickels. Which system

### 4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag.

ALGEBRA 1 Fall 2016 Semester Exam Review Name 1. According to the data shown below, which would be the best prediction of the average cost of a -bedroom house in Georgetown in the year 2018? Year Average

### Systems of Equations Unit Five ONE NONE INFINITE

Systems of Equations Unit Five ONE NONE INFINITE Standards: 8.EE.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables

### Name Class Date. Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations?

Name Class Date 1-1 1 Variables and Expressions Going Deeper Essential question: How do you interpret, evaluate and write algebraic expressions that model real-world situations? A-SSE.1.1a ENGAGE Interpreting

### Applications of Systems of Equations

Applications of Systems of Equations Procedure for Solving Application Problems. 1. Read the problem carefully. 2. Determine the unknowns and assign variable(s) to them. 3. Set up your equation(s). 4.

### Indiana Core 40 End-of-Course Assessment Algebra I Blueprint*

Types of items on the Algebra I End-of-Course Assessment: Multiple-choice 1 point per problem The answer to the question can be found in one of four answer choices provided. Numeric response 1 point per

### Math 1 Variable Manipulation Part 4 Word Problems

Math 1 Variable Manipulation Part 4 Word Problems 1 TRANSLATING FROM ENGLISH INTO ALGEBRA (PLUG IN) The next part of variable manipulation problems is to figure out the problem from real life situations.

### Get Ready. 8. Graph each line. Choose a convenient method.

Get Ready BLM... Substitute and Evaluate. Evaluate each expression when x = 4 and y =. a) x + 4y b) x y c) 4x + y + 5 d) x y. Evaluate each expression when a = and b =. a) a b + 4 b) a + b 7 c) a b d)

### Practice EOC Questions

Practice EOC Questions 1 One of the events at a high school track meet is the pole vault. The pole vaulter runs toward the crossbar and uses a pole to attempt to vault over the bar. Josh collects data

### ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Algebra 1 S1 (#2201) and Foundations in Algebra 1 S1 (#7769)

Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Ramal goes to the grocery store and buys pounds of apples and pounds of bananas. Apples cost dollars per

### Introduction to Systems of Equations

Systems of Equations 1 Introduction to Systems of Equations Remember, we are finding a point of intersection x 2y 5 2x y 4 1. A golfer scored only 4 s and 5 s in a round of 18 holes. His score was 80.

### Math 1 Unit 7 Review

Name: ate: 1. Which ordered pair is the solution to this system of equations? 5. system of equations is graphed on the set of axes below. y = x + 4 x + y = 2. (1, 5). (0, 2). ( 1, 3). ( 4, 0) 2. Which

### Algebra I EOC Packet #

1. Simplify: A 60x 2.5 B 60x 3 C 16x 2.5 D 16x 3 2. If y varies directly as x, and y = 12 when x = 72, then what is the value of x when y = 3? A 18 B 2 C D 3. Which expression is the greatest common factor

### Final Exam Study Guide

Algebra 2 Alei - Desert Academy 2011-12 Name: Date: Block: Final Exam Study Guide 1. Which of the properties of real numbers is illustrated below? a + b = b + a 2. Convert 6 yards to inches. 3. How long

### AFDA Review of Equations

Identify the choice that best completes the statement or answers the question. 1. Which expression correctly represents the area of the rectangle above? a. x² + 2 b. 6(x + 2) c. (x + 2)(x + 6) d. 8x 2.

### Algebra Practice Set. *Evaluate number and algebraic expressions using rational numbers and Order of Operations

Algebra Practice Set Expressions *Evaluate number and algebraic expressions using rational numbers and Order of Operations *Translate algebraic expressions into words using appropriate language *Write

### Fall IM I Exam B

Fall 2011-2012 IM I Exam B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations is linear? a. y = 2x - 3 c. 2. What is the

### SHOW ALL WORK ON SEPARATE PAPER Answers will be provided at a later date. REAL NUMBER SYSTEM Go back and try problems on Review 1 and Test 1.

07 Accelerated Fall Exam Review Name: SHOW ALL WORK ON SEPARATE PAPER Answers will be provided at a later date. REAL NUMBER SYSTEM Go back and try problems on Review and Test.. Name the set(s) of numbers

### Algebra 1 STAAR EOC Review #7 Reporting Category 4: Linear Equations and Inequalities

Name Class Date RC3 A.07A Algebra 1 STAAR EOC Review #7 Reporting Category 4: Linear Equations and Inequalities 1. Passengers on many commercial flights may make calls from a telephone provided by the

### Writing and Solving Equations

Writing and Solving Equations Melody s Music Solution Lesson 6-1 Modeling and Writing Two-Step Equations ACTIVITY 6 Learning Targets: Use variables to represent quantities in real-world problems. Model

### 1 st : Read carefully and underline key words 2 nd : Write a let statement 3 rd : Determine whether to use,,, or 4 th : Write and solve the inequality

Name Period: Represent each of the following as an algebraic inequality. 1) x is at most 30 2) the sum of 5x and 2x is at least 14 3) the product of x and y is less than or equal to 4 4) 5 less than a

### Applications of Systems of Linear Equations

5.2 Applications of Systems of Linear Equations 5.2 OBJECTIVE 1. Use a system of equations to solve an application We are now ready to apply our equation-solving skills to solving various applications

### Name Date Class. Solving Equations by Adding or Subtracting

2-1 Practice A Solving Equations by Adding or Subtracting Solve each equation by using addition. Check your answers. 1. m 2 = 5 2. t 9 = 14 3. p 6 = 2 4. a 4.5 = 3.5 5. 3 = c 8 6. y 1 5 = 2 5 Solve each

### MATH 1710 College Algebra Final Exam Review

MATH 1710 College Algebra Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) There were 480 people at a play.

### Expressions & Equations Chapter Questions. 6. What are two different ways to solve equations with fractional distributive property?

Expressions & Equations Chapter Questions 1. Explain how distribution can simplify a problem. 2. What are like terms? 3. How do you combine like terms? 4. What are inverse operations? Name them. 5. How

### 3.1 NOTES Solving Systems of Linear Equations Graphically

3.1 NOTES Solving Systems of Linear Equations Graphically A system of two linear equations in two variables x and y consist of two equations of the following form: Ax + By = C Equation 1 Dx + Ey = F Equation

### 5, 0. Math 112 Fall 2017 Midterm 1 Review Problems Page Which one of the following points lies on the graph of the function f ( x) (A) (C) (B)

Math Fall 7 Midterm Review Problems Page. Which one of the following points lies on the graph of the function f ( ) 5?, 5, (C) 5,,. Determine the domain of (C),,,, (E),, g. 5. Determine the domain of h

### A.7A Mini-Assessment

LGER I (.) Linear Functions. The formulates equations and inequalities based on linear functions, uses a variet of methods to solve them, and analzes the solutions in terms of the situation. The student

### Math 112 Spring 2018 Midterm 1 Review Problems Page 1

Math Spring 8 Midterm Review Problems Page Note: Certain eam questions have been more challenging for students. Questions marked (***) are similar to those challenging eam questions.. Which one of the

### 4) Solve for this system using your graphing

Algebra Unit 5 HW Day 1 SOLVING GRAPHICALLY Graph the following systems: 1) x 2y 12 y 2x 6 2) y x 2 6x 2y 10 ) x y 9 4) Solve for this system using your graphing x calculator. [You will still need to put

### 1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined?

Graphing Linear Equations Chapter Questions 1. What are the various types of information you can be given to graph a line? 2. What is slope? How is it determined? 3. Why do we need to be careful about

### Name Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16

Name Algebra 1 Date Midterm Review Period 1) Solve each equation: a) x 2x + 2 = 3 b) 5 5 + 9 = 13 c) 64 = 9x +1 d) x 7 2 = 10 4x e) x + 2 3 = 3x 2) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16 3) Solve and

### Chapter 6 review. 1. Which statement is true about the graphs of these equations?

Name: Date: 1. Which statement is true about the graphs of these equations? y = 6x + 4 y = 5x 2 A. The lines intersect, but are not perpendicular. B. The lines are parallel. 4. Members of a senior class

### Pre-Algebra 8 Semester 1 Practice Exam

. Evaluate xy when x = 0 and y = 6. 6 80. Which expression is equivalent to x + x x + x+ x+ x+ x x x x x x x?. In math class, we follow the order of operations when evaluating expressions. Which is the

### 8 th Grade Domain 2: Algebra and Functions (40%) Sara

8 th Grade Domain 2: Algebra and Functions (40%) 1. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line and tell

### Inequalities Chapter Test

Inequalities Chapter Test Part 1: For questions 1-9, circle the answer that best answers the question. 1. Which graph best represents the solution of 8 4x < 4 A. B. C. D. 2. Which of the following inequalities

### Algebra 1 Fall Review

Name Algebra 1 Fall Review 2013-2014 Date 1. Write an inequality to best represent the graph shown at right. (A.1.D.) m: b: inequality: 2. Write an inequality to best describe the graph shown at right.

### Why? Speed Skating Tracks offi cial track short track

Applying Systems of Linear Equations Then You solved systems of equations by using substitution and elimination. (Lessons 6-2, 6-3, and 6-4) Now 1Determine the best method for solving systems of 2Apply

### 1. The sum of four consecutive even numbers is 52. What is the largest of these numbers?

1. The sum of four consecutive even numbers is 52. What is the largest of these numbers? 26 22 C 16 10 2. In a high school basketball game, Sarah scored 10 points in the first half of the game. In the

### Question 4: Expand and simplify: (x - 4) (x - 6) Answer: x 2-10x Question 1: Expand and simplify: (x + 3) (x + 8) Answer: x x + 24

astle Algebra L1 Got the answer? e the first to stand with your group s flag. Got it correct? MAKE or REAK a castle, yours or any other group s. The group with the most castles wins. Enjoy! Question 1:

### Define the word inequality

Warm Up: Define the word inequality Agenda: Objective- Students can solve linear inequalities in one variable, including equations with coefficients represented by letters. Define Inequalities One & Two

### f) 3r + 5 = Solve each equation in question 1. Explain why you chose the method you did.

Extra Practice 1A Lesson 6.1: Solving Equations 1. Look at the algebraic expressions and equations below. Which are expressions? Equations? How do you know? a) 2m + 3 b) x + 4 = 8 c) 2z 1 = 3 d) y 3x 1

### Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1

Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Summer 2013 Solving Linear Equations Student Packet Day 3 Name: Date: Benchmark MA.912.A.3.1 Solve linear equations in one variable that include simplifying

### Algebra 1 Fall Semester Final Review Name

It is very important that you review for the Algebra Final. Here are a few pieces of information you want to know. Your Final is worth 20% of your overall grade The final covers concepts from the entire

### No. Items Working Column Mark

TEST 16 291 No. Items Working Column Mark 1. Write in figures: Seven hundred and two thousand and nine. 702 009 Answer 2. Multiply: 124 by 25 124 x 25 = 3100 Answer 3. Express 0.375 as a percent. Answer

### a. Bob: 7, Bridget: 4, Brian 1 b. Bob: 7, Bridget: 4, Brian 3 c. Bob: 7, Bridget: 14, Brian 3 a. 100 b. 150 c c. 2 d.

Period: Date: K. Williams 8th Grade Year Review: Chapters -4. A neighborhood pool charges \$22 for a pool membership plus an additional \$2 for each visit to the pool. If Elliot visited the pool 6 times,

### 4-A5: Mid-Chapter 4 Review

-A: Mid-Chapter Review Alg H Write the equations for the horizontal and vertical lines that pass through the given point.. (, 0) Horiz. Vert.. (0, 8) Horiz. Vert. Use the slope formula to find the slope

### Algebra 1 STAAR Review Name: Date:

Algebra 1 STAAR Review Name: Date: 1. Which graph does not represent y as a function of x? I. II. III. A) I only B) II only C) III only D) I and III E) I and II 2. Which expression is equivalent to? 3.

### UNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:

UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities

### Chapter 4 - Writing Linear Functions

Chapter 4 - Writing Linear Functions Write an equation of the line with the given slope and y-intercept. 1. slope: 3 y-intercept: 6 a. y = 6x + 3 c. y = 6x 3 b. y = 3m + 6 d. y = 3x 6 2. D REF: Algebra

### A = LW V = LWH. P = a + b + c T = CN + F. d = rt P = 2(L +W ) = 2L + 2W 635 = 2N N / N = 510 / N N = 255

Free Pre-Algebra Lesson 18! page 1 Lesson 18 Writing Equations for Word Problems Math on the Street New York City math teacher George Nobl had a table in Times Square where he gave out candy bars to passers-by

### 4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

Name: Period: Date: Algebra 1 Common Semester 1 Final Review Like PS4 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3.

### Algebra I Item Sampler (Updated April 2011)

Algebra I Item Sampler (Updated April 011) Purpose The purpose of this Item Sampler is to provide teachers and students with examples of the types of questions that will appear on the ISTEP+: Algebra I

### Algebra I Solving & Graphing Inequalities

Slide 1 / 182 Slide 2 / 182 Algebra I Solving & Graphing Inequalities 2016-01-11 www.njctl.org Slide 3 / 182 Table of Contents Simple Inequalities Addition/Subtraction click on the topic to go to that

### Pre-Algebra Semester 1 Practice Exam A

. Evaluate xy when x 0 and y 6. 6 80. Which expression is equivalent to x x x xxx x x xxx x x?. In math class, we follow the order of operations when evaluating expressions. Which is the second operation

### Algebra 1 S1 (#2201) Foundations in Algebra 1 S1 (#7769)

Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: Algebra 1 S1 (#2201) Foundations

### Math 7 Homework # 46 M3 L1

Name Date Math 7 Homework # 46 M3 L1 Lesson Summary Terms that contain exactly the same variable symbol can be combined by addition or subtraction because the variable represents the same number. Any order,

### 4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the

### ALGEBRA I END-OF-COURSE EXAM: PRACTICE TEST

Page 1 ALGEBRA I END-OF-COURSE EXAM: PRACTICE TEST 1. Order the following numbers from least to greatest:, 6, 8.7 10 0, 19 b. 19,, 8.7 100, 6 6, 8.7 10 0,, 19 c. d. 8.7 10 0,, 19, 6, 6, 19, 8.7 100. If

### UNIT 2 SOLVING EQUATIONS

UNIT 2 SOLVING EQUATIONS NAME: GRADE: TEACHER: Ms. Schmidt _ Solving One and Two Step Equations The goal of solving equations is to. We do so by using. *Remember, whatever you to do one side of an equation.

### Instructional Materials for WCSD Math Common Finals

Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following courses: High School Algebra 1 S1

### Equations & Inequalities Chapter Questions. 3. What are two different ways to solve equations with fractional distributive property?

Equations & Inequalities Chapter Questions 1. What are inverse operations? Name them. 2. How do you solve equations? 3. What are two different ways to solve equations with fractional distributive property?

### Part 1 1 st 6weeks material

Name Date Period Part 1 1 st 6weeks material 1. Write an expression that can be used to determine the number of blocks in the n th figure. 2. Write an expression to represent the sequence below: 5, 8,

### Math5900 Final Review

Math5900 Final Review. Find the formula to predict any term in this sequence and then find the 5 th number in this sequence -,, 9, 5,... Answer: either a n =6 n if you start counting at n=0 OR a n =6 n

### SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES

5 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES I. INTRODUCTION AND FOCUS QUESTIONS Have you ever asked yourself how businessmen make profits? How can farmers increase their yield or harvest?

### Semester 1 Final Review. c. 7 d.

Solve the equation in questions 1-4. 1. 7 x + 5 = 8 a. 7 b. 1 7 c. 7 d. 7. 7 = d + 0 a. 10 b. 0 c. 1 d. 1. p 1 = 5(p 1) (7 p) a. b. 0 c. 9 d. 10 4. 5x 5 = x 9 a. b. 1 c. 1 d. 5. A customer went to a garden

### Extra Practice Chapter 5. Topics Include: Direct & Partial Variation Slope Slope as a Rate of Change First Differences

Extra Practice Chapter 5 Topics Include: Direct & Partial Variation Slope Slope as a Rate of Change First Differences 5.1 - Practice: Direct Variation 1. Find the constant of variation for each direct

### PROJECT - Systems of Equations and Matrix Equations

PROJECT - Systems of Equations and Matrix Equations NAME AND CLASS PERIOD Due on: If turned in by _ by 4:15, you may earn 5 extra points. To earn 5 more extra points, make up your own WORD PROBLEM for

### Equations can be classified according to the types of operations and quantities involved. Important types include:

UNIT 5. EQUATIONS AND SYSTEM OF EQUATIONS EQUATIONS An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions

### Name Date Class. 5 y x + 7

Name Date Class 7.EE.1 SELECTED RESPONSE Select the correct answer. 1. What property allows the expression.7x + 10. + 15.3x 8.x + 15.6 to be simplified to the equivalent expression 0x + 10. 8.x + 15.6?

### Solve Linear Systems by Substitution

5.2 Solve Linear Systems by Substitution Systems of linear equations can be used to help determine the best selling price for products and services. Investigate A Class Problem Tools graphing calculator

### Pre-Algebra Semester 1 Practice Exam B DRAFT

. Evaluate x y 5 6 80 when x = 0 and y =.. Which expression is equivalent to? + + + +. In Pre-Algebra class, we follow the order of operations in evaluating expressions. Which operation should a student

### c. Solve the system of two equations to find the speed of the boat in the water (x) and the speed of the current (y). (0.45, 0.05)

Math Applications The applications that follow are like the ones you will encounter in many workplaces. Use the mathematics you have learned in this chapter to solve the problems. Wherever possible, use

### Algebra 1 End-of-Course Assessment Practice Test with Solutions

Algebra 1 End-of-Course Assessment Practice Test with Solutions For Multiple Choice Items, circle the correct response. For Fill-in Response Items, write your answer in the box provided, placing one digit

### Study Guide and Intervention

NAME DATE PERIOD Study Guide and Intervention Algebra: Equations An equation is a sentence in mathematics that contains an equals sign. The solution of an equation is the value that when substituted for

### WRITING EQUATIONS through 6.1.3

WRITING EQUATIONS 6.1.1 through 6.1.3 An equation is a mathematical sentence that conveys information to the reader. It uses variables and operation symbols (like +, -, /, =) to represent relationships

### c. (4abc 2 ) 0 6. Solve the following equations, and name the properties used for each step.

Name: CC Algebra 9H Midterm Review Date:. Simplify the following: (3x + x 3) (x 5x + 7) (9 t t ) (8t + t ). Simplify the following (x + )(3x 8x + ) (x 3) c. (x + ) 3 3. Simplify the following using the

### Math 803. Unit 1: Solving Equations in One Variable (8.EE.7) Part 2

Math 803 Unit 1: Solving Equations in One Variable (8.EE.7) Part 2 1.4 Variables on both sides (2.4 text) 1.5 Solve multi-step equations (2.5 text) Name: Period: Teacher s Name: 1 Lesson 1.4 Equations

### Algebra - Chapter 5 Review

Name Hour Algebra - Chapter 5 Review 1. Write an equation in slope-intercept form of the graph. 10 y 10 x 10 2. The cost of a school banquet is \$95 plus \$15 for each person attending. Write an equation

### On Your Own. Applications. Unit 1. 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars.

Applications 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars. 2 t = 0.5 + 2a, where a represents the area of the grass and t represents the time in hours

### Unit 2 Day 3 MATRICES. MATRIX Applications Quiz 1

Unit 2 Day 3 MATRICES MATRIX Applications Quiz 1 Remember: Phones OFF Warm-Up and in Blue Pockets! Check the list. Tracey, Danica, and Sherri bought snacks for a girls sleepover. They each bought the items

### Chapter 3. Q1. Show that x = 2, if = 1 is a solution of the system of simultaneous linear equations.

Chapter 3 Q1. Show that x = 2, if = 1 is a solution of the system of simultaneous linear equations. Q2. Show that x = 2, Y = 1 is not a solution of the system of simultaneous linear equations. Q3. Show

### Midterm: Wednesday, January 23 rd at 8AM Midterm Review

Name: Algebra 1 CC Period: Midterm: Wednesday, January 23 rd at 8AM Midterm Review Unit 1: Building Blocks of Algebra Number Properties (Distributive, Commutative, Associative, Additive, Multiplicative)

### FSA Algebra I End-of-Course Review Packet. Algebra and Modeling

FSA Algebra I End-of-Course Review Packet Algebra and Modeling Table of Contents MAFS.912.A-APR.1.1 EOC Practice... 3 MAFS.912.A-CE1.1 EOC Practice... 5 MAFS.912.A-REI.2.3 EOC Practice... 7 MAFS.912.A-CE1.4

### Materials for assessing adult numeracy

Materials for assessing adult numeracy Number Task The population of Wales is approximately Write this in numbers in the box. million. What is the value of the 7 in this number? Write your answer in words.

### Winter-Break Packet 7 th grade mathematics

M.S. 181 PABLO CASALS CHRISTOPHER WARNOCK, PRINCIPAL 800 BAYCHESTER AVENUE, BRONX, NY 10475 PHONE: 718-904-5600 Conceive, it, Believe it, Achieve it! Winter-Break Packet 7 th grade mathematics Student:

### More with Systems of Equations

More with Systems of Equations In 2008, 4.7 million Americans went on a rafting expedition. In Georgia, outfitters run whitewater expeditions for ages 8 and up on the Chattooga River. 12.1 Systems of Equations

### Math 141:512. Practice Exam 1 (extra credit) Due: February 6, 2019

Math 141:512 Due: February 6, 2019 Practice Exam 1 (extra credit) This is an open book, extra credit practice exam which covers the material that Exam 1 will cover (Sections 1.3, 1.4, 2.1, 2.2, 2.3, 2.4,

### A C E. Applications. Applications Connections Extensions. Student 1 Student Below are some results from the bridge experiment in a CMP class.

A C E Applications Connections Extensions Applications 1. Below are some results from the bridge experiment in a CMP class. Bridge-Thickness Experiment Number of Layers 2 4 6 8 Breaking Weight (pennies)

### BLoCK 4 ~ LIneAr equations

BLoCK 4 ~ LIneAr equations systems OF equations Lesson 22 parallel, intersecting or THe same Line ---------------------------- 129 Explore! Types of Systems Lesson 23 solving systems BY graphing -----------------------------------------

### Solve Problems with Equations

Develop Skills and Strategies Part 1: Introduction Solve Problems with Equations CCSS 7.EE.B. 7.EE.B.4a You know how to compute with rational numbers and write and solve one-step equations. Take a look

### Review: Expressions and Equations

Review: Expressions and Equations Expressions Order of Operations Combine Like Terms Distributive Property Equations & Inequalities Graphs and Tables Independent/Dependent Variables Constant: a number