Question

A shop sells bicycles and tricycles. In total there

are 7 cycles and 19 wheels. Determine how many of each there
are, if a bicycle has two wheels and a tricycle has three wheels

Answer 1

There are 2 bicycles and 3 tricycles.

Explanation:

Set up 2 equations, let x be the number of bicycles and y be the number of tricycles.

There are total of 7 cycles in the shop:

x + y = 7

There is a total of 19 wheels in the shop:

2x + 3y = 19

We can now solve for a system of equations:

x + y = 7

2x+ 3y = 19

I just chose to solve for y first:

x = -y+7

2(-y+7) + 3y = 19

-2y + 14 + 3y = 19

y = 5

Go back and plug y into any equation:

x + 5 = 7

x = 2

Therefore, there are two bicycles and three tricycles