SOLUTION: There are 15 total bicycles and tricycles and there is a total of 37 wheels. How many tricycles are there?

Question 664371: There are 15 total bicycles and tricycles and there is a total of 37 wheels. How many tricycles are there?
Found 2 solutions by Theo, lynnlo:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
total of 15 bicycles and tricycles
total of 37 wheels.
how many tricycles?

let x = number of bicycles
let y = number of tricycles

x + y = 15 (number of bicycles + number of tricycles = 15)
2x + 3y = 37 (number of bicycle wheels + number of tricycle wheels = 37)

you need to solve these 2 equations simultaneously.
use one of the equations to solve for y
use that value of for y to replace y in the second equation.

we'll solve for y in the equation of x + y = 15 because it's easier to do.
start with x + y = 15
subtract x from both sides of the equation to get y = 15 - x

replace y with 15 - x in the second equation.
second equation is 2x + 3y = 37
replace y with 15 - x to get 2x + 3 * (15 - x) = 37
simplify to get 2x + 45 - 3x = 37
combine like terms to get -x + 45 = 37
subtract 45 from both sides of the equation to get -x = 37 - 45
simplify to get -x = -8
divide both sides of the equation by -1 to get x = 8
since x + y = 15 and x = 8, then 8 + y = 15.
solve for y to get y = 7.
you now have x = 8 and y = 7
substitute 8 for x and 7 for y in both equations to confirm that these solutions are good.
x + y = 15 becomes 8 + 7 = 15 which becomes 15 = 15 which is true.
2x + 3y = 37 becomes 2*8 + 3*7 = 37 which becomes 16 + 21 = 37 which becomes 37 = 37 which is true.
the solutions for x and y are good.
x = 8
y = 7
question is how many tricycles are there?
answer is 7 because y represents the number of tricycles.

Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!
37wheels
tricyles================7 x 3 wheels=21
bikes===================8 x 2 wheels=16
=========================================
total bikes========15=====wheels=37
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