Mr Flynn 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 ¹₃ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₆ of a pizza and the girls had 5¹₂ pizzas left. How many pizzas did Mr Flynn buy?

	Girls (1)	Boys (2)
Before	2 u	1 u
Change	- 1 p	- 2 p
After	33	0

¹₃ = ²₆

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 2 slices of pizza.

Number of slices that the girls had left
= 5¹₂ ÷ ¹₆ 
= ¹¹₂ x 6
= 33

2 u - 1 p = 33 --- (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 = 33
4 p - 1 p = 33
3 p = 33

1 p = 33 ÷ 3 = 11

Total number of slices of pizzas for girls
= 33 + 1 p
= 33 + 11
= 44

Total number of slices of pizzas for boys
= 44 ÷ 2
= 22

Total number of slices of pizzas for students
= 44 + 22
= 66

Total number of pizzas that Mr Flynn bought
= 66 ÷ 6
= 11

Answer(s): 11