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I need help with this math problem. 10 points to a correct answer WITH EXPLANATION!!!!!!? |
At Irv's Cycle Rental Shop, Irv rents all kinds of cycles: unicycles, tandem bikes, regular bikes, and even tricycles for little kids. He parks all the cycles in front of his shop with a helmet for each rider strapped to the cycles. This morning Irv counted 57 helmets and 115 wheels parked in front of his store. He knows he has an equal number of unicycles and tandem bikes. He also knows that he has 32 regular bikes. How many unicycles, tandem bikes, and tricycles does Irv have? Note: For a tandem bicycle you will need 2 helmets (while all the other cycles only need 1) Let x = number of unicycles, then x = tandem bikes since he has an equal number of unicycles and tandem bikes 32 = regular bikes Let y = tricycles For helmets x(1) +x(2) +32(1) +y(1) = 57 or 3x + y + 32 = 57 or 3x + y = 25 Also, for number of tires x(1) + x(2) + 32(2) + y(3) = 115 or 3x + 3y = 51 or x + y = 17 You have two equations 3x+y = 25 and x +y = 17 Subtract the second from the first 2x = 8 or x = 4 then y = 13 Answer: 4 unicycles, 4 tandem bikes, 32 regular bikes, and 13 tricycles Check: For number of helmets: 4 + 4(2) + 32 + 13 = 4+8+32+13 = 57 For tires: 4(1) + 4(2) + 32(2) + 13(3) = 4+8+64+39 = 115 You have 32 reg bikes=64 tires 115-64=51 you have 7 trikes=21 tires 51-21=30 which gives you 10 tandem bikes=20 tires and 10 unis=10 tires 20+10=30 so its 32 reg, 10 uni, 10 tandem, 7 trikes |
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