Mr Vincent bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 2 times as many pizzas as the boys. Each boy ate ¹₂ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₆ of a pizza and the girls had 13¹₃ pizzas left. How many pizzas did Mr Vincent buy?

	Girls (1)	Boys (2)
Before	2 u	1 u
Change	- 1 p	- 3 p
After	80	0

¹₂ = ³₆

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

Number of slices that the girls had left
= 13¹₃ ÷ ¹₆ 
= ⁴⁰₃ x 6
= 80

2 u - 1 p = 80 --- (1)

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

Make u the same.

(2)_x2
2 u = 6 p --- (3)

Substitute (3) into (1).
2 u - 1 p = 80
6 p - 1 p = 80
5 p = 80

1 p = 80 ÷ 5 = 16

Total number of slices of pizzas for girls
= 80 + 1 p
= 80 + 16
= 96

Total number of slices of pizzas for boys
= 96 ÷ 2
= 48

Total number of slices of pizzas for pupils
= 96 + 48
= 144

Total number of pizzas that Mr Vincent bought
= 144 ÷ 6
= 24

Answer(s): 24