SOLUTION: Here is the question in its exact words, There are a different number of bicycles, tandem bicycles, and tricycles in the Wheel Shop. There are a total of 135 seats, 118 front ha

Question 120313: Here is the question in its exact words,
There are a different number of bicycles, tandem bicycles, and tricycles in the Wheel Shop. There are a total of 135 seats, 118 front handle bars (that steer the bike), and 269 wheels. How many are bicycles, tandem bicycles, and tricycles are there in the Wheel Shop? (Hint: A tandem bike has two seats. Bicycles and tricycles have one seat. All of the cycles have one set of front handle bars that steer the bike. A bicycle and tandem bike have two wheels. A tricycle has three wheels.).
Please try to solve this as soon as possible,
Thank You
Found 2 solutions by checkley71, scott8148:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
135=1T+1B+2TB
-(118=T+B+TB) NOW SUBTRACT EQUATION 2 FROM EQAUTION 1.
----------------------------
17=TB IS THE NUMBER OF TANDEM BIKES.
269=3T+2B+2*17
269=3T+2B+34
269-34=3T+2B
235=3T+2B NUMBER OF WHEELS.
118=T+B+17
118-17=T+B
101=T+B NUMBER OF HANDLE BARS. NOW MULTIPLY THIS EQUATION BY -2 AND ADD TO THE WHEEL EQUATION:
235=3T+2B
-202=-2T-2B
------------------
33=T OR THE NUMBER OF TRICYCLES.
118=33+B+17
118-33-17=B
68=B OF THE NUMBER OF BIKES.
PROOF
269=3*33+2*68+2*17
269=99+136+34
269=269

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
there are 118 cycles (118 front handlebars @ one each)

there are 17 more seats than cycles (135-118), so there are 17 tandem bicycles

there are 33 more wheels than twice the number of cycles [269-(2*118)], so there are 33 tricycles

this means that there are 68 bicycles (118-17-33)
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