Question

VERY DIFFICULT WORD PROBLEM.

A Bike has 1 Handlebar, 2 Pedals and 2 Wheels.
A Tricycle has 1 Handlebar, 2 Pedals, and 3 Wheels.
A Tandem Bike has 1 Handlebar, 4 Pedals, and 2 Wheels.

If a Bikeshop has a total of 144 Handlebars, 378 Pedals and 320 Wheels, how many Bicycles, Tandem Bikes, and Tricycles does it have?


Please at show work, or explain how to solve this.

Answer 1

Let B be the number of bikes, T the number of trikes, and D the number of tandems.
There are B+T+D=144 handlebars, 2B+2T+4D=378 pedals, and 2B+3T+2D=320 wheels. Solve the system to get your answer. :)

Answer 2

I'm not too sure what to do from that point on...

Answer 3

Here, I'll start:
\[\begin{cases}
B+T+D=144 \qquad &1\\
2B+2T+4D=378 &2\\
2B+3T+2D=320 &3
\end{cases}\]
Divide equation 2 by 2:
\[B+T+2D=189\]
Subtract equation 1 from this:
\[D=189-144=45\]
Therefore, from the very first equation:
\[B+T=144-45=99\]
Now subtract equation 2 from 3:
\[T-2D=-58\\
T=-58+2D=32\]
Can you determine what B is now? :)

Answer 4

...I think I get it...
...Is B... 67?

Answer 5

Right-o! :)

Answer 6

Then T must be 32, and D must be 45!
Thank you!

Answer 7

You're welcome. :D