Mr Andy bought some pizzas for a group of pupils. There was an equal number of boys and girls. The boys received 5 times as many pizzas as the girls. Each girl ate ¹₂ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₆ of a pizza and the boys had 9¹₃ pizzas left. How many pizzas did Mr Andy buy?

	Boys (1)	Girls (2)
Before	5 u	1 u
Change	- 1 p	- 3 p
After	56	0

¹₂ = ³₆

Cutting the slices of pizzas into same size. Each pizza was cut into 6 slices. Every boy ate 1 slice of pizza and every girl ate 3 slices of pizza.

Number of slices that the boys had left
= 9¹₃ ÷ ¹₆ 
= ²⁸₃ x 6
= 56

5 u - 1 p = 56 --- (1)

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

Make u the same.

(2)_x5
5 u = 15 p --- (3)

Substitute (3) into (1).
5 u - 1 p = 56
15 p - 1 p = 56
14 p = 56

1 p = 56 ÷ 14 = 4

Total number of slices of pizzas for boys
= 56 + 1 p
= 56 + 4
= 60

Total number of slices of pizzas for girls
= 60 ÷ 5
= 12

Total number of slices of pizzas for pupils
= 60 + 12
= 72

Total number of pizzas that Mr Andy bought
= 72 ÷ 6
= 12

Answer(s): 12