Mr Peter bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 5 times as many pizzas as the boys. Each boy ate ¹₃ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₆ of a pizza and the girls had 13¹₂ pizzas left. How many pizzas did Mr Peter buy?

	Girls (1)	Boys (2)
Before	5 u	1 u
Change	- 1 p	- 2 p
After	81	0

¹₃ = ²₆

Cutting the slices of pizzas into same size. Each pizza was cut into 6 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 ÷ ¹₆ 
= ²⁷₂ x 6
= 81

5 u - 1 p = 81 --- (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 = 81
10 p - 1 p = 81
9 p = 81

1 p = 81 ÷ 9 = 9

Total number of slices of pizzas for girls
= 81 + 1 p
= 81 + 9
= 90

Total number of slices of pizzas for boys
= 90 ÷ 5
= 18

Total number of slices of pizzas for pupils
= 90 + 18
= 108

Total number of pizzas that Mr Peter bought
= 108 ÷ 6
= 18

Answer(s): 18