Mr Tom bought some pizzas for a group of children. There was an equal number of girls and boys. The girls received 4 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 ¹₁₈ of a pizza and the girls had 7¹₃ pizzas left. How many pizzas did Mr Tom buy?

	Girls (1)	Boys (2)
Before	4 u	1 u
Change	- 1 p	- 3 p
After	132	0

¹₆ = ³₁₈

Cutting the slices of pizzas into same size. Each pizza was cut into 18 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.

Number of slices that the girls had left
= 7¹₃ ÷ ¹₁₈ 
= ²²₃ x 18
= 132

4 u - 1 p = 132 --- (1)

1 u - 3 p = 0
1 u = 3 p --- (2)

Make u the same.

(2)_x4
4 u = 12 p --- (3)

Substitute (3) into (1).
4 u - 1 p = 132
12 p - 1 p = 132
11 p = 132

1 p = 132 ÷ 11 = 12

Total number of slices of pizzas for girls
= 132 + 1 p
= 132 + 12
= 144

Total number of slices of pizzas for boys
= 144 ÷ 4
= 36

Total number of slices of pizzas for children
= 144 + 36
= 180

Total number of pizzas that Mr Tom bought
= 180 ÷ 18
= 10

Answer(s): 10