A bicycle and tricycle is shipped in its own box. Oddly, the manufacturer shipped all the wheels in a separate box. If there are 16 boxes of bicycles/tricycles total, and 45 wheels total, how many tricycles were ordered?

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Answer 1 · 2016-02-21T00:09:21

Bicycles = 3
Tricycles = 13

May the number of bicycles = "b" and tricycles = "t".

If there are 16 boxes, it means that the total number of bicycles and tricycles is equal to 16, or:

#b + t = 16#

For each bicycle there are 2 wheels and for each tricycle there are 3 wheels. Therefore

#2*b + 3*t = 45#

We have now a system with two equations:

#{(b+t = 16),(2b+3t=45):}#

Solving the system:

#b = 16 - t#

Substituting "b" in the second equation:

#2(16-t)+3t=45#
#32-2t+3t=45#
#t=45-32#

#t=13# (number of tricycles)

#b= 16-13#

#b = 3# (number of bicycles)