Mr Ken bought some pizzas for a group of children. There was an equal number of girls and boys. The girls received 5 times as many pizzas as the boys. Each boy ate ¹₄ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₈ of a pizza and the girls had 13¹₂ pizzas left. How many pizzas did Mr Ken buy?

	Girls (1)	Boys (2)
Before	5 u	1 u
Change	- 1 p	- 2 p
After	108	0

¹₄ = ²₈

Cutting the slices of pizzas into same size. Each pizza was cut into 8 slices. Every girl ate 1 slice of pizza and every boy ate 2 slices of pizza.

Number of slices that the girls had left
= 13¹₂ ÷ ¹₈ 
= ²⁷₂ x 8
= 108

5 u - 1 p = 108 --- (1)

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

Make u the same.

(2)_x5
5 u = 10 p --- (3)

Substitute (3) into (1).
5 u - 1 p = 108
10 p - 1 p = 108
9 p = 108

1 p = 108 ÷ 9 = 12

Total number of slices of pizzas for girls
= 108 + 1 p
= 108 + 12
= 120

Total number of slices of pizzas for boys
= 120 ÷ 5
= 24

Total number of slices of pizzas for children
= 120 + 24
= 144

Total number of pizzas that Mr Ken bought
= 144 ÷ 8
= 18

Answer(s): 18