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## 7.4 HW Answers

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**(4, -1)**(19, 16) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. (5, 3) (5, 6) (-½, -2) (-7, -12) (9, -3) (2, 1) (-10, -5) (4, 4)**10x + 2y = 155**12x + 3y = 189 $14.50 balls $5 bags**x = -19 + 9**x = -10 5(y + 9) – 3y = 7 y = -19 (-10, -19)**Scoring Your Homework**Count how many problems you missed or didn’t do 0-1 missed = 10 2-3 missed = 9 4-5 missed = 8 6-7 missed = 7 8-9 missed = 6 • 10-11 missed = 5 • 12-13 missed = 4 • 14-15 missed = 3 • 16-17 missed = 2 • 18-19 missed = 1 • 20-21 missed = 0**Table of Contents**Topic Page # ... 7.1 Solve Systems By Graphing 76 7.2 Solve Systems By Substitution 77 7.3 Solve Systems By Combination 78 7.4 Multiplication w/ Combination 79 7.5 System Word Problems 80**You are selling tickets to a play. The price of a student**ticket is $5, and the price of an adult ticket is $8. You sell 556 tickets and you collect $3,797. How many adult and student tickets did you sell? Step 1: Choose your variables S = student ticket a = adult ticket**You are selling tickets to a play. The price of a student**ticket is $5, and the price of an adult ticket is $8. You sell 556 tickets and you collect $3,797. How many adult and student tickets did you sell? Step 2: Write two equations: A) One that represents the value of the items 5s + 8a = 3797 B) One that represent the quantity of items s + a = 556**Step 3: Solve the system using substitution or elimination**5s + 8a = 3797 5s + 8a = 3797 + (–8) s + a = 556 -8s – 8a = -4448 -3s = -651 217 + a = 556 s = 217 a = 339**2. A bag contains dimes and nickels. There are 18 coins in**the bag. The value of the coins is $1.25. How many of each type of coin is in the bag? Step 1: Choose your variables d = # dimes n = # nickels**2. A bag contains dimes and nickels. There are 18 coins in**the bag. The value of the coins is $1.25. How many of each type of coin is in the bag? Step 2: Write two equations: A) One that represents the value of the items 0.10d + 0.05n = 1.25 B) One that represent the quantity of items d + n = 18**Step 3: Solve the system using substitution or elimination**(100) 10d + 5n = 125 0.10d + 0.05n = 1.25 + (–5) d + n = 18 -5d – 5n = -90 5d = 35 7 + n = 18 d = 7 n = 11**3. Kylie has 4.50 in dimes and quarters. She has 3 more**dimes than quarters. How many quarters does she have? d = # dimes q = # quarters 0.10d + 0.25q = 4.50 d = q + 3 = 12 + 3 = 15 0.10(q + 3) + 0.25q = 4.50 0.35q = 4.20 0.10q + 0.30 + 0.25q = 4.50 q = 12 0.35q + 0.30 = 4.50**4. An adult ticket to a school play costs $5 and a student**ticket costs $3. A total of $460 was collected from the sale of 120 tickets. How many student tickets were purchased? a = adult ticket s = student ticket 5a + 3s = 460 a + s = 120**5a + 3s = 460**5a + 3s = 460 + (–3) a + s = 120 -3a – 3s = -360 2a = 100 a = 50 50 + s = 120 s = 70**5. A drummer goes to Guitar Center and buys drum sticks**and brushes. The wood sticks that he buys are $10.50 a pair, and the brushes are $24 a pair. He buys twice as many pairs of wood sticks as brushes, and ends up spending a total of $90. How many pair of sticks and brushes did he buy? d = drum sticks b = brushes 10.50d + 24b = 90 d = 2b**10.50d + 24b = 90**= 2(2) = 4 d = 2b 10.50(2b) + 24b = 90 21b + 24b = 90 45b = 90 b = 2**6. The sophomore class is selling pretzels and popcorn at a**school event to raise money for a dance. They charge $2.50 for a bag of popcorn and $2 for a pretzel. They collect $336 during the event. They sell twice as many bags of popcorn as pretzels. How many pretzels do they sell? z = pretzels p = popcorn 2.50p + 2z = 336 p = 2z**2.50p + 2z = 336**p = 2z = 2(48) = 96 2.50(2z) + 2z = 336 5z + 2z = 336 7z = 336 z = 48**7. You went to Home Depot and bought two types of plants.**One type was a flowering plant while the other was non-flowering. The flowering plant cost $3.20 each and the non-flowering plant cost $1.50 each. You purchased a total of 24 plants for $49.60. How many of each type of plant did he buy? f = flower plant n = non-flower 3.20f + 1.5n = 49.60 f + n = 24**(10)**32f + 15n = 496 3.20f + 1.5n = 49.60 + (–15) f + n = 24 -15f – 15n = -360 17f = 136 8 + n = 24 f = 8 n = 16