Mr Julian bought some pizzas for a group of students. There was an equal number of girls and boys. The girls received 5 times as many pizzas as the boys. Each boy ate ¹₄ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₁₂ of a pizza and the girls had 9¹₃ pizzas left. How many pizzas did Mr Julian buy?

	Girls (1)	Boys (2)
Before	5 u	1 u
Change	- 1 p	- 3 p
After	112	0

¹₄ = ³₁₂

Cutting the slices of pizzas into same size. Each pizza was cut into 12 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.

Number of slices that the girls had left
= 9¹₃ ÷ ¹₁₂ 
= ²⁸₃ x 12
= 112

5 u - 1 p = 112 --- (1)

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

Make u the same.

(2)_x5
5 u = 15 p --- (3)

Substitute (3) into (1).
5 u - 1 p = 112
15 p - 1 p = 112
14 p = 112

1 p = 112 ÷ 14 = 8

Total number of slices of pizzas for girls
= 112 + 1 p
= 112 + 8
= 120

Total number of slices of pizzas for boys
= 120 ÷ 5
= 24

Total number of slices of pizzas for students
= 120 + 24
= 144

Total number of pizzas that Mr Julian bought
= 144 ÷ 12
= 12

Answer(s): 12