5-3B Systems Review Puzzle
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1 5-3B Systems Review Puzzle x + y = 4 x y = -2 2x + y = -4 2x + 3y = 4 2x + y = 1 4x 2y = 6 2x + y = 1 x + y = 1 3x 2y = 4-2x + 2y = -1 x = -2y = x + y y = 2 2x x = y 5 y = 4 + 3x 2x + 1 = y x y = 2 y = 4 2x B M E F C D H D H D G M B F B F E B C H O D H O H D G M B F B I E D O M A O N B O H I K B E B F H D G I D E C H D M B K M F M A H D O H O H D N B K B B I F I A H D O O D N M F B K M E B E M O H D H O F I I M F B I E M E H O H D D B F B F B F M F B M A D O H N M I M B K I B I F E M A O N I K F I F M E M E M I B I M F M F B K I B C O G B O K F H M D J F D G H H L D F H M B O I H O B H A D O I O I D L I D F O L M O I O A (-1, 4) I (2, 1) B (-1, 3) J (2, 0) C (0, 1) K (-3, -4) D (-4, 4) L (-3, -5) E (0, -1) M (-3, 1) F (3, 5/3) N (7, -3) G (3, 5/2) O (1, -1) H (1, 3)
2 5-3C Word Problems (Class Work) Word Problems: Linear Systems Using Substitution (PP) Solve these word problems by defining 2 different variables and writing 2 equations. Then, use substitution or elimination to solve each system. EXAMPLE: Jenny has 8 moving boxes that she can use to pack for college. Each box can hold 15 pounds of clothing or 60 pounds of books. If Jenny is moving 255 pounds how many boxes of each type are there? Define Variables: Number Let c = number of clothes boxes Let b = number of book boxes Define Variables: Weight Let 15c = weight of clothing boxes Let 60b = weight of book boxes Verbal Model: number # of clothing boxes + # of book boxes = total # of boxes Equation: number c + b = 8 Verbal model: weight weight of clothing boxes + weight of book boxes = total weight Equation: weight 15c + 60b = 255 c + b = 8 15c + 60b = 255 Solution: 3 book boxes and 5 clothing boxes. #1 In one day the museum collected $1590 from 321 people. The price of admission is $6 for an adult and $4 for a child. How many adults and how many children were admitted to the museum? Define Variables: Number Define Variables: Value Verbal Model: number Equation: number Verbal model: value Equation: value
3 #2 An investor bought 225 shares of stock. Stock A was purchased at $50 per share and Stock B at $75 per share. If $13,750 worth of stock was purchased, how many shares of each kind of stock did the investor buy? Define Variables: Number Define Variables: Value Verbal Model: number Equation: number Verbal model: value Equation: value # 3 The length of a rectangle is 1 m more than twice its width. If the perimeter is 110 meters, find the dimensions. Define Variables: Verbal Model: Equation Verbal Model: Perimeter Equation: Perimeter
4 Complete the following problems. Use the same format as the examples. Practice 1: A sightseeing boat charges $5 for children and $8 for adults. On its first trip of the day, it collected $439 for 71 paying passengers. How many children and how many adults were there? Define Variables: Verbal Model: Equation Verbal Model: Value Equation: Value Practice 2: The length of a rectangle is 12 inches more than twice its width. If the perimeter is 90 inches, what are the dimensions of the rectangle? Define Variables: Verbal Model: Equation Verbal Model: Perimeter Equation: Perimeter
5 5-3C Wkst Alg 1CP 5-5B Review: Linear Systems and Problem Solving (Class Work - PP) Alg. 1CP Follow the PowerPoint to solve each problem using a system of Linear Equations. 1. A class has a total of 25 students. Twice the number of girls is equal to 3 times the number of boys. How many boys and girls are there in the class? 2. The length of a rectangle is 4 m more than twice its width. If the perimeter is 38 m, find the dimensions. 3. The cost of an adult ticket for the talent show was $2. The cost of a student ticket was $1.50. The total income from the ticket sales was $550. The number of adult tickets sold was 100 less than 3 times the number of student tickets. How many tickets of each type were sold? 4. The number of quarters that Tom has is 3 times the number of nickels he has. All together, he has $1.60. How many quarters and how many nickels does he have?
6 Work with a partner to continue solving these problems using Linear Systems. 5. The sum of two numbers is 100. Five times the smaller number is 8 more than the larger number. What are the two numbers? 6. One number is 12 more than half another number. The two numbers have a sum of 60. Find the numbers. 7. If you buy six pens and one mechanical pencil, you ll get $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you ll get $2 change. How much does each pen and pencil cost?
7 5-5B HW Solving Word Problems Using Two Variables Alg. 1CP On a separate paper: Define variables and write a system of equations for each problem. Use whatever variables seem appropriate. THEN SOLVE THE SYSTEM OF EQUATIONS. Remember to label the solutions. 1. Richard and Connie purchased a radio for $128. Richard paid $36 more than Connie. How much did each pay? 2. Annette and June bowled together and had a combined score of 425. June s score was 25 less than Annette s score. Find their scores. 3. Steve has $3 more than twice as much as Tracy. Together they have $57. How much money does each person have? 4. The length of a rectangle is 5 cm less than three times its width. If the perimeter is 70 cm, find the dimensions. 5. The sum of two numbers is 83. Four times the smaller number is 8 less than the larger number. Find the numbers.
8 Ch. Rev. A More Word Problems (cont. from yesterday) Write a system of equations for each problem. Use whatever variables seem appropriate. THEN SOLVE THE SYSTEM OF EQUATIONS. Remember to label the solutions. 6. Paul has 30 coins in dimes and quarters. Their total value is $4.50. How many coins of each type does he have? 7. Sally has $21.40 in dimes and quarters for a total of 100 coins. How many of each kind of coin does Sally have? 8. A movie theater charges $5 for an adult s ticket and $2 for a child s ticket. One Saturday the theater sold 785 tickets for $3280. How many children s tickets were sold for the movie that Saturday? 9. The cost of an adult ticket to a football game was $1.75. The cost of a student ticket was $1.25. The number of student tickets sold was twice the number of adult tickets. The total income from the sale of tickets was $850. How many tickets of each type were sold? 10. Gary is five times as old as Frank. One third of the sum of their ages is equal to 32. Find their ages.
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