Mr Michael bought some pizzas for a group of students. 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 8¹₃ pizzas left. How many pizzas did Mr Michael buy?

	Girls (1)	Boys (2)
Before	2 u	1 u
Change	- 1 p	- 3 p
After	50	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
= 8¹₃ ÷ ¹₆ 
= ²⁵₃ x 6
= 50

2 u - 1 p = 50 --- (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 = 50
6 p - 1 p = 50
5 p = 50

1 p = 50 ÷ 5 = 10

Total number of slices of pizzas for girls
= 50 + 1 p
= 50 + 10
= 60

Total number of slices of pizzas for boys
= 60 ÷ 2
= 30

Total number of slices of pizzas for students
= 60 + 30
= 90

Total number of pizzas that Mr Michael bought
= 90 ÷ 6
= 15

Answer(s): 15