Mr David 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 ¹₁₈ of a pizza and the boys had 8⁵₉ pizzas left. How many pizzas did Mr David buy?

	Boys (1)	Girls (2)
Before	5 u	1 u
Change	- 1 p	- 3 p
After	154	0

¹₆ = ³₁₈

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

Number of slices that the boys had left
= 8⁵₉ ÷ ¹₁₈ 
= ⁷⁷₉ x 18
= 154

5 u - 1 p = 154 --- (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 = 154
15 p - 1 p = 154
14 p = 154

1 p = 154 ÷ 14 = 11

Total number of slices of pizzas for boys
= 154 + 1 p
= 154 + 11
= 165

Total number of slices of pizzas for girls
= 165 ÷ 5
= 33

Total number of slices of pizzas for pupils
= 165 + 33
= 198

Total number of pizzas that Mr David bought
= 198 ÷ 18
= 11

Answer(s): 11