SOLUTION: a toy museum has a collection of bicycles and tricycles. together they have 36 pedals and 43 wheels. how many tricycles does the museum have

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: a toy museum has a collection of bicycles and tricycles. together they have 36 pedals and 43 wheels. how many tricycles does the museum have      Log On


   

Question 938086: a toy museum has a collection of bicycles and tricycles. together they have 36 pedals and 43 wheels. how many tricycles does the museum have
Found 2 solutions by Stitch, ewatrrr:
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let B = number of bicycles
Let T = number of tricycles
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Both types only have two pedals each.
So 36 total pedals divide by 2 mean there are only 18 devices in the museum.
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Lets write a couple equations.
Equation 1: B+%2B+T+=+18
Equation 2: 2B+%2B+3T+=+43
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Solve equation 1 for one of the variables.
B+%2B+T+=+18
B+=+18+-+T
Plug (18-T) into equation 2 for B
Equation 2: 2B+%2B+3T+=+43
2%2A%2818-T%29+%2B+3T+=+43
Simplify
36+-+2T+%2B+3T+=+43
Combine like terms.
36+%2B+T+=+43
Subtract 36 from both sides.
highlight%28T+=+7%29
There are 7 tricycles in the museum.
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You can now solve for B as well by plugging 7 in for T
B+=+18+-+T
B+=+18+-+%287%29
highlight_green%28B+=+11%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
2b + 3t = 43
-1(2b + 2t = 36)
t = 7, number of tricycles. And, bicycles = 11 18-7
...
and...checking
2•11 + 3•7 = 22 + 21 = 43 wheels