In a shop, There are 25 bicycles and tricycles. There are 63 wheels in all. Find the number of bicycles in the shop.

Answer 1

b + t = 25
2 b + 3 t = 63

3 b + 3 t = 75
2 b + 3 t = 63
---------------subtract
1 b + 0 = 12
b = 12

Answer 2

Let bicycles = x, and tricycles = y

The algebraic equation using the number of wheels and the number of tricycles and bicycles is:

x + y = 25
2x + 3y = 63
I can multiply the top equation by two and subtract from the second one:
2x + 3y = 63
-(2x + 2y = 50)

which gives

y = 13 tricycles

Finally, I substitute y into the equation and I get x = 12 bikes

There are 12 bicycles and 13 tricycles in the shop.