SOLUTION: Question: The Wheel shop sells other kinds of vehicles. There are bicycles and go-carts in a different room of the shop. Each bicycle has only one seat and each go-cart has on

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Question 161618: Question:
The Wheel shop sells other kinds of vehicles. There are bicycles and go-carts in a different room of the shop. Each bicycle has only one seat and each go-cart has only one seat. There are a total of 21 seats and 54 wheels in that room. Bicyle has 2 wheels and go-carts have 4 wheels. How many bicycles and how many are go-carts? Explain how you figured it out.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
let x = number of bicycles
let y = number of go karts
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each bicycle has 1 seat and 2 wheels.
each go kart has 1 seat and 4 wheels.
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total number of seats is 21.
seats equation is
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1*x + 1*y = 21
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total number of wheels is 54.
wheels equation is
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2*x + 4*y = 54
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solve these two equations simultaneously to get x and y.
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multiply seats equation by 2 on both sides to make it
2*x + 2*y = 42
subtract seats equation from wheels equation.
2*x + 4*y = 54 = wheels equation
- 2*x + 2*y = 42 = seats equation
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= 0*x + 2*y = 12
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equation becomes
2*y = 12
y = 6
if y = 6, then x + y = 21 becomes x + 6 = 21 becomes x = 15
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x = 15
y = 6
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substitute for x and y in seats equation
15 + 6 = 21 = ok
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substitute for x and y in wheels equation
2*15 + 4*6 = 54
30 + 24 = 54
54 = 54 = ok
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answer is:
number of bicycles is 15
number of go karts is 6
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