There are a total of 144 front steering handlebars, 378 pedals, and 320 wheels. How many bicycles, tricycles, and tandem bikes are in the shop?

Question

Bicycles have 1 seat, 2 pedals, and 2 wheels. Tricycles have 1 seat, 2 pedals, and 3 wheels. Tandem Bikes have 2 seats, 4 pedals, and 2 wheels. 

Answer 1

 

Let's say there are x bicycles, y tricycles, and z tandem bikes.

 

Then, we can come up with the following set of equations.

 

     x + y + z = 144           (Eq. 1)

 

     2x + 2y + 4z = 378        (Eq. 2)

 

     2x + 3y + 2z = 320        (Eq. 3)

 

If we multiply Eq. 1 by 4 and then subtract Eq. 2 from it, we get

 

     x + y = 99                  (Eq. 4)

 

If we multiply Eq. 1 by 2 and then subtract it from Eq. 3, we get

 

     y = 32

 

If we put y = 32 into Eq. 4, we get

 

     x = 67

 

If we put x = 67 and y = 32 into Eq. 1, we get

 

     z = 45

 

So, there 67 bicycles, 32 tricycles, and 45 tandem bikes in the shop.