Mr Howard bought some pizzas for a group of pupils. There was an equal number of boys and girls. The boys received 2 times as many pizzas as the girls. Each girl ate ¹₃ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₆ of a pizza and the boys had 10¹₂ pizzas left. How many pizzas did Mr Howard buy?

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

¹₃ = ²₆

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 2 slices of pizza.

Number of slices that the boys had left
= 10¹₂ ÷ ¹₆ 
= ²¹₂ x 6
= 63

2 u - 1 p = 63 --- (1)

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

Make u the same.

(2)_x2
2 u = 4 p --- (3)

Substitute (3) into (1).
2 u - 1 p = 63
4 p - 1 p = 63
3 p = 63

1 p = 63 ÷ 3 = 21

Total number of slices of pizzas for boys
= 63 + 1 p
= 63 + 21
= 84

Total number of slices of pizzas for girls
= 84 ÷ 2
= 42

Total number of slices of pizzas for pupils
= 84 + 42
= 126

Total number of pizzas that Mr Howard bought
= 126 ÷ 6
= 21

Answer(s): 21