Mr Valen bought some pizzas for a group of children. There was an equal number of boys and girls. The boys received 4 times as many pizzas as the girls. Each girl ate ¹₅ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₁₅ of a pizza and the boys had 15²₅ pizzas left. How many pizzas did Mr Valen buy?

	Boys (1)	Girls (2)
Before	4 u	1 u
Change	- 1 p	- 3 p
After	231	0

¹₅ = ³₁₅

Cutting the slices of pizzas into same size. Each pizza was cut into 15 slices. Every boy ate 1 slice of pizza and every girl ate 3 slices of pizza.

Number of slices that the boys had left
= 15²₅ ÷ ¹₁₅ 
= ⁷⁷₅ x 15
= 231

4 u - 1 p = 231 --- (1)

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

Make u the same.

(2)_x4
4 u = 12 p --- (3)

Substitute (3) into (1).
4 u - 1 p = 231
12 p - 1 p = 231
11 p = 231

1 p = 231 ÷ 11 = 21

Total number of slices of pizzas for boys
= 231 + 1 p
= 231 + 21
= 252

Total number of slices of pizzas for girls
= 252 ÷ 4
= 63

Total number of slices of pizzas for children
= 252 + 63
= 315

Total number of pizzas that Mr Valen bought
= 315 ÷ 15
= 21

Answer(s): 21