SOLUTION: 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

Question 582626: 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.
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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,
320 wheels?
------------------------------------------------
How many bicycles, tricycles, and tandem bikes?
----
Wheels Eq: 2b + 3t + 2tb = 320
Pedals Eq: 2b + 2t + 4tb = 378
HandbarEq: 1b + 1t + 1tb = 144
----------------------------
I used the Matrix function on my TI-84 to get:
b = 67 bikes
t = 32 tricycles
tb = 45 tandem bikes
===========================
Cheers,
Stan H.
=================
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

"378 pedals" ___ 2x + 2y + 4z = 378

"320 wheels" ___ 2x + 3y + 2z = 320
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