Mr Liam bought some pizzas for a group of children. There was an equal number of girls and boys. The girls received 3 times as many pizzas as the boys. Each boy ate ¹₆ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₁₂ of a pizza and the girls had 7¹₂ pizzas left. How many pizzas did Mr Liam buy?

	Girls (1)	Boys (2)
Before	3 u	1 u
Change	- 1 p	- 2 p
After	90	0

¹₆ = ²₁₂

Cutting the slices of pizzas into same size. Each pizza was cut into 12 slices. Every girl ate 1 slice of pizza and every boy ate 2 slices of pizza.

Number of slices that the girls had left
= 7¹₂ ÷ ¹₁₂ 
= ¹⁵₂ x 12
= 90

3 u - 1 p = 90 --- (1)

1 u - 2 p = 0
1 u = 2 p --- (2)

Make u the same.

(2)_x3
3 u = 6 p --- (3)

Substitute (3) into (1).
3 u - 1 p = 90
6 p - 1 p = 90
5 p = 90

1 p = 90 ÷ 5 = 18

Total number of slices of pizzas for girls
= 90 + 1 p
= 90 + 18
= 108

Total number of slices of pizzas for boys
= 108 ÷ 3
= 36

Total number of slices of pizzas for children
= 108 + 36
= 144

Total number of pizzas that Mr Liam bought
= 144 ÷ 12
= 12

Answer(s): 12