Solve the following word problem.

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Solve the following word problem. The perimeter of a rectangle is 24. The width is 2 times its length. Find the dimensions of the rectangle. Let: L = length W = width 2L + 2W = 24 Solve the system W = 2L 2L + 2(2L) = 24 W = 2L 2L + 4L = 24 W = 2(4) 6L = 24 W = 8 L = 4 Length is 4 and Width is 8

11.04 Using Systems to solve Word Problems (Coin / Money)

To solve a word problem using a system: 1) read the problem carefully 2) assign variables and set up a system 3) solve the system 4) answer the question A word problem that involves money will have decimals in the equations when you set up the system. Remove the decimals by multiplying all the terms by 100.

Solve the following word problem. A man has 18 coins in his pocket, all dimes and quarters. When counted, he has $3.60. How many of each coin are there? Let: d = dimes q = quarters d + q = 18 Solve the system .10d + .25q = 3.60 Clear the decimals from the 2nd equation, multiply by 100. d + q = 18 d + q = 18 10d + 25q = 360 d + 12 = 18 10d + 10q = 180 d = 6 – 10d – 25q = – 360 __________________ – 15q = – 180 q = 12 6 Dimes and 12 Quarters

Solve the following word problem. The difference of the value of dimes and nickels is $0.60. The sum of the value of dimes and nickels is $1.40. How many of each coin are there? Let: n = nickels d = dimes .10d – .05n = .60 Solve the system .10d + .05n = 1.40 Clear the decimals from both equations, multiply by 100. 10d – 5n = 60 10d + 5n = 140 10d + 5n = 140 __________________ 10(10) + 5n = 140 20d = 200 100 + 5n = 140 5n = 40 d = 10 n = 8 10 Dimes and 8 Nickels

Solve the following word problem. Six apples and 3 bananas cost $4.95. Six apples and 5 bananas cost $5.45. Find the cost of each apple and each banana. Let: a = apples b = bananas 6a + 3b = 4.95 Solve the system 6a + 5b = 5.45 Clear the decimals from both equations, multiply by 100. 600a + 300b = 495 6a + 3b = 4.95 600a + 500b = 545 6a + 3(.25) = 4.95 600a + 300b = 495 6a + 0.75 = 4.95 – 600a – 500b = – 545 6a = 4.20 ____________________ a = 0.70 – 200b = – 50 b = 0.25 Apples $0.70 Bananas $0.25

Solve the following word problem. 3 adult tickets and 4 child tickets cost $24.25. 5 adult tickets and 3 child tickets cost $31.25. Find the cost of each adult and child ticket. Let: a = adult c = child 3a + 4c = 24.25 Solve the system 5a + 3c = 31.25 Clear the decimals from both equations, multiply by 100. 300a + 400c = 2425 3a + 4c = 24.25 500a + 300c = 3125 3a + 4(2.50) = 24.25 1500a + 2000c = 12125 3a + 10.00 = 24.25 – 1500a – 900c = – 9375 3a = 14.25 ______________________ a = 4.75 1100c = 2750 c = 2.50 Adult $4.75 Child $2.50