In a shop, there are 25 bicycles and tricycles. there are 63 wheels in all. find the numbers of bicycles and tricycles in the shop.

let x be number of bicycles

and y the number of tricycles

So

x + y = 25 equation 1

The number of wheels is

2x + 3y = 63 equation 2

We can multiply the equation 1 by two and subtract from the second one ...

2x + 3y = 63

- (2x + 2y = 50)

then

y = 13 trikes and

x = 12 bikes