Question

christopher is walking past a bike shop and looks inside. He sees some bicycles and some tricycles. He sees 32 seats and 77 wheels. How many tricycles are in the shop.

Answer 1

• Bicycles: 1 seat and 2 wheels
• Tricycles: 1 seat and 3 wheels

So with this, we will be making a system of equations. One representing the amount of seats and one representing the amount of wheels. Let x = bicycles and y = tricycles:

`x+y=32\\2x+3y=77`

With this, I will be using the substitution method. Firstly, subtract y on both sides of the first equation:

`x=32-y\\2x+3y=77`

Next, substitute x in the second equation for (32 - y) and solve for y:

`2(32-y)+3y=77\\64-2y+3y=77\\64+y=77\\y=13`

In short, there are 13 tricycles.

Answer 2

A bicycle has 2 wheels and a tricycle has 3 wheels. Both have only 1 seat so he saw a total of 32 bikes.

Let "x" represent the number of bicycles and "y" represent the number of tricycles. The solution below is using the substitution method.

x + y = 32 → x = 32 - y

2x + 3y = 77 → 2(32 - y) + 3y = 77 → 64 - 2y + 3y = 77 → 64 + y = 77 → y = 13

Answer: 13 tricycles