SOLUTION: Sorry, but I have to repeat the other question I have put because I need the equation to only use ONE variable, to be able to be solved by hand: There are three types of bikes.

Question 582661: Sorry, but I have to repeat the other question I have put because I need the equation to only use ONE variable, to be able to be solved by hand:
There are three types of bikes. A bicycle, tricycle, and tandem bikes. A bicycle as 2 wheels, 2 pedals, and 1 seat. A tricycle has 3 wheels, 2 pedals, and 1 seat. A tandem bike has 2 wheels, 4 pedals, and 2 seats.
How many of each are there if there are 144 front steering handlebars, 378 pedals, and 320 wheels? How many bicycles, tricycles, and tandem bikes?
Can you tell me the equation to find it? It's been bugging me for a while.
Ex: 2x + 2(320 - x) + ? = # of bikes or something.
Found 2 solutions by scott8148, KMST:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x=bikes, y=trikes, and z=tandems

"there are 144 front steering handlebars" ___ x + y + z = 144 (A)

"378 pedals" ___ 2x + 2y + 4z = 378 (B)

"320 wheels" ___ 2x + 3y + 2z = 320 (C)

subtracting 2(A) from (B) ___ 2z = 90 ___ z = 45

subtracting 2(A) from (C) ___ y = 32

subtracting y and z from (A) ___ x = 67
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
We can do one variable at a time, but you need to find three numbers that mean different things (number of bicycles, number of tricycles, and number of tandem bikes), so I would rather use three different letter for those numbers. We could re-use old traditional x, for each part of the problemm, but it could get confusing.
The total number of bikes is the number of front steering handlebars: 144.
How many tricycles?
Tricycles are the only bikes with 3 wheels. All the other bikes have 2.
So if we call the number of tricycles x, the number of other bikes (bicycles and tandem bikes) will be 144-x
The number of wheels will be

Let's find x:
--> (applying distributive property)
--> --> (collecting like terms, which is also the distributive property)
--> -->
How many tandem bikes?
Tandem bikes have 4 pedals, while all the other bikes have just 2.
Do you want to call the number of tandem bikes y? We could call it x, if we remember that we are recycling and this x is not the same x as before, but I'd rather use a different letter.
If the number of tandem bikes is y, the number of other bikes (bicycles and tricycles) is 144-y.
The total number of pedals is

Let's find y:
--> --> --> --> --> --> -->
So we know there are 32 tricycles and 45 tandem bikes.
How many bicycles.
If z is the number of bicycles, the total number of bikes is
--> --> -->
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