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

Transcription

1 Intensive Math-Algebra I Mini-Lesson MA.912.A.3.1 Summer 2013 Solving Linear Equations Student Packet Day 3

2

3 Name: Date: Benchmark MA.912.A.3.1 Solve linear equations in one variable that include simplifying algebraic expressions Also assesses MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality. This benchmark will be assessed using MC and FR items. Students will: Solve linear equations in one variable. Content Limits Equations must be presented in all items. Items may include equations with the variable on both sides of the equation. Items may include applications of commutative, associative, distributive, and identity properties. Lesson MA.912.A.2.4 Textbook: Prentice Hall Algebra 1 I can Solve linear equations in one variable. Vocabulary Properties of Equality Inverse Operations Equivalent Equations Identity Essential Understanding To solve linear equations, you can use the properties of the equality and inverse operations to form a series of simpler equivalent equations. You can use the properties of the equality repeatedly to isolate the variable. Example # 1: Textbook page: 89 Guided Practice: Textbook page 91: and page 92: Example # 2: Textbook page 89 Guided Practice: Textbook page 91: and page 92: 58

4 Example # 3: Textbook page 94 Guided Practice: Textbook page 98: Example # 4: Textbook page 95 Guided Practice: Textbook page 98: and page 99: Example # 5: Textbook page 96 Example # 6: Textbook page 102 Guided Practice: Textbook page 98: 24 26, page 99: 64 65, and page 106: Small Group Practice 1. Clarissa bought enough fencing to border either a rectangular or triangular garden, as shown in the figure below. If the gardens have the same perimeter, the following equation can be used to solve this situation. 2(3x 3) + 2(x 3) = 2x 1 + 2x 1 + 2x Which of the following represents the number of feet of fencing that Clarissa bought? A. 5 B. 14 C. 24 D The Art Club is going on a field trip to the local modern art museum. Tickets to the museum cost $8.00 for museum members and $10.00 for non-members. The total cost of the field trip for the 22 Art Club students was $ The equation below represents this situation, where x is the number of students who are museum members. 8x + 10(22 x) = 208 Which of the following represents the number of students who are museum members? A. 6 B. 9 C. 12 D. 16

5 3. Pauline works as a sales representative for a book publishing company. Her monthly salary is calculated as follows: In this equation, S = her monthly salary and d = dollars of sales. (Pauline has always managed to sell at least $6,000 worth of books each month.) Last month, her salary was $2,594. How many dollars worth of sales did she have? 4. The average length of a Florida bonnethead shark is about 42 inches. The average length is 12.5 inches more than 0.5 times the maximum length, m. This is given by the equation 42 = m. What is the maximum length of a Florida bonnethead shark in inches? 5. Sandi and Felipe are participating in a Walk for Life to raise money for charity. Sandi will raise $30, plus $2.50 for each mile she walks. Felipe will raise $20, plus $5 for each mile he walks. The total amount that each will raise can be calculated using the following expressions, where n stands for the number of miles walked: Sandi: n Felipe: 20 5n After how many miles will Sandi and Felipe have raised the same amount of money? Small Group Practice: Focus Practice MA912A31 Mini-Assessment MA912A31 Score: Home Learning: HL MA912A31

6 Focus Practice MA.912.A What is the value of x in the equations below? a) b) c) d) ( ) 2. The instructions for baking a turkey recommend cooking a 12-pound bird for 30 minutes in a 350 degree oven. The instructions also suggest adding 3 extra minutes of cooking time for each additional pound. The cooking time for a turkey can be calculated using the equation below, where w represents the weight of the turkey. If Maria needs to cook her turkey for 45 minutes, how many pounds does Maria's turkey weigh? 3. An airline company charges $200 per flight, regardless of the destination. The company also charges $25 dollars for every piece of luggage. In addition, they charge $0.02 for every mile of the flight. With only one piece of luggage, the total cost of the trip can be calculated using the equation below, where x represents the number of miles in the flight. If a trip costs $325, how many miles long is the flight?

7 4. Lena sells earrings from a booth at the arts fair. She pays $200 to rent the booth. She makes $5 from each pair of earrings she sells. Her profit, P, can be found using the following equation, where n is the number of pairs of earrings sold. How many pairs of earrings must Lena sell to earn a profit of $450? 5. Before buying a new washer and dryer Henrico used to spend $60.00 a month doing his laundry at the Laundromat. The equation where is the cost of buying a new washer and dryer can be used to determine the number of months,, it would take for the washer and dryer to pay for themselves. How much money did Henrico spend on the washer and dryer if it took 36 months for the washer and dryer to pay by themselves? 6. Pauline works as a sales representative for a book publishing company. Her monthly salary is calculated as follows: In this equation, S = her monthly salary and d = dollars of sales. (Pauline has always managed to sell at least $6,000 worth of books each month.) Last month, her salary was $2,594. How many dollars worth of sales did she have? 7. What is the value of x in the equation? 8. Sandi and Felipe are participating in a Walk for Life to raise money for charity. Sandi will raise $30, plus $2.50 for each mile she walks. Felipe will raise $20, plus $5 for each mile he walks. The total amount that each will raise can be calculated using the following expressions, where n stands for the number of miles walked: After how many miles will Sandi and Felipe have raised the same amount of money?

8 Home Learning MA A.3.1 Solving Linear Equations in One Variable 1. Solve the linear equation: A -36 B -1 C 18 D 2 2. Solve the linear equation. Where necessary, choose no solution or all real numbers. F -11 G 11 H 10 I Solve the linear equation. Where necessary, choose no solution or all real numbers. A p = -33 B p = -35 C p = -68 D p = Select the appropriate property being demonstrated. F Associative Property of Multiplication G Associative Property of Addition H Distributive Property I Commutative Property of Multiplication 5. Select the appropriate property being demonstrated. A Commutative Property of Multiplication B Identity Property of Multiplication C Distributive Property D Associative Property of Multiplication 6. Solve the linear equation. Where necessary, choose no solution or all real numbers. F no solution G -8 H 8 I all real numbers 7. Solve the linear equation. Where necessary, choose no solution or all real numbers. A all real numbers B -213 C the empty set D 13

9 8. Marcos reads at an average rate of 30 pages per hour, while Mindy reads at an average rate of 40 pages per hour. If Marcos starts reading a novel at 4:30 PM, and Mindy begins reading the same novel at 5:20 PM, at what time will they be reading the same page? 9. In order to break his record, Joe Big league must get at least 280 hits this season. In the second to last week of the season, Joe had 266 hits and got 8 more. How many hits must Joe get in the season s last week? 10. The daily cost of renting a car is $25.00 plus $0.50 per mile traveled. If Emily paid $ for one day rental, how many miles did she travel? 11. Sam and Orlando have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Orlando. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell? 12. Jane and her friends were selling cookies. They sold 4 more boxes the second week than they did the first. On the third week, they doubled the sale of their second week. Altogether, they sold a total of 352 boxes. How many boxes did they sell in the third week?