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7.4 HW Answers 1. (4, -1) 6. (19, 16) 2. (5, 3) 7. (5, 6) 3. (-½, -2) 8. (-7, -12) 4. (9, -3) 9. (2, 1) 5. (-10, -5) 10. (4, 4) 10x + 2y = 155 12x + 3y = 189 $14.50 balls $5 bags 2 y x2 3 (-2, -2) x = -19 + 9 5(y + 9) – 3y = 7 y = -19 x = -10 (-10, -19) 5x 6 7 7 5 x 6 7 1 13 x 5 5 -1/5 0 13/5 x3 8 x 3 8 or x 3 8 x 5 or x 11 -11 0 5 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 ... 7.1 7.2 7.3 7.4 7.5 Page # Solve Systems By Graphing Solve Systems By Substitution Solve Systems By Combination Multiplication w/ Combination System Word Problems 76 77 78 79 80 1. 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 1. 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 (–8) s + a = 556 217 + a = 556 a = 339 + 5s + 8a = 3797 -8s – 8a = -4448 -3s = -651 s = 217 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) 0.10d + 0.05n = 1.25 (–5) d + n = 18 7 + n = 18 n = 11 + 10d + 5n = 125 -5d – 5n = -90 5d = 35 d=7 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 0.10q + 0.30 + 0.25q = 4.50 0.35q + 0.30 = 4.50 0.35q = 4.20 q = 12 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 (–3) a + s = 120 + 5a + 3s = 460 -3a – 3s = -360 2a 50 + s = 120 s = 70 = 100 a = 50 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 d = 2b = 2(2) = 4 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) 3.20f + 1.5n = 49.60 (–15) f + n = 24 8 + n = 24 n = 16 32f + 15n = 496 + -15f – 15n = -360 17f = 136 f=8