Mr Warren 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 ¹₆ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₁₂ of a pizza and the boys had 5¹₄ pizzas left. How many pizzas did Mr Warren buy?

	Boys (1)	Girls (2)
Before	5 u	1 u
Change	- 1 p	- 2 p
After	63	0

¹₆ = ²₁₂

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

Number of slices that the boys had left
= 5¹₄ ÷ ¹₁₂ 
= ²¹₄ x 12
= 63

5 u - 1 p = 63 --- (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 = 63
10 p - 1 p = 63
9 p = 63

1 p = 63 ÷ 9 = 7

Total number of slices of pizzas for boys
= 63 + 1 p
= 63 + 7
= 70

Total number of slices of pizzas for girls
= 70 ÷ 5
= 14

Total number of slices of pizzas for pupils
= 70 + 14
= 84

Total number of pizzas that Mr Warren bought
= 84 ÷ 12
= 7

Answer(s): 7