Mr Archie 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 ¹₆ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₁₂ of a pizza and the girls had 10¹₂ pizzas left. How many pizzas did Mr Archie buy?

	Girls (1)	Boys (2)
Before	5 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 girl ate 1 slice of pizza and every boy ate 2 slices of pizza.

Number of slices that the girls had left
= 10¹₂ ÷ ¹₁₂ 
= ²¹₂ x 12
= 126

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

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

Make u the same.

(2)_x5
5 u = 10 p --- (3)

Substitute (3) into (1).
5 u - 1 p = 126
10 p - 1 p = 126
9 p = 126

1 p = 126 ÷ 9 = 14

Total number of slices of pizzas for girls
= 126 + 1 p
= 126 + 14
= 140

Total number of slices of pizzas for boys
= 140 ÷ 5
= 28

Total number of slices of pizzas for students
= 140 + 28
= 168

Total number of pizzas that Mr Archie bought
= 168 ÷ 12
= 14

Answer(s): 14