Mr Liam bought some pizzas for a group of students. There was an equal number of boys and girls. The boys received 4 times as many pizzas as the girls. Each girl ate ¹₆ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₁₂ of a pizza and the boys had 10¹₂ pizzas left. How many pizzas did Mr Liam buy?

	Boys (1)	Girls (2)
Before	4 u	1 u
Change	- 1 p	- 2 p
After	126	0

¹₆ = ²₁₂

Cutting the slices of pizzas into same size. Each pizza was cut into 12 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 ÷ ¹₁₂ 
= ²¹₂ x 12
= 126

4 u - 1 p = 126 --- (1)

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

Make u the same.

(2)_x4
4 u = 8 p --- (3)

Substitute (3) into (1).
4 u - 1 p = 126
8 p - 1 p = 126
7 p = 126

1 p = 126 ÷ 7 = 18

Total number of slices of pizzas for boys
= 126 + 1 p
= 126 + 18
= 144

Total number of slices of pizzas for girls
= 144 ÷ 4
= 36

Total number of slices of pizzas for students
= 144 + 36
= 180

Total number of pizzas that Mr Liam bought
= 180 ÷ 12
= 15

Answer(s): 15