Mr Paul bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 3 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 ¹₁₈ of a pizza and the girls had 6²₃ pizzas left. How many pizzas did Mr Paul buy?

	Girls (1)	Boys (2)
Before	3 u	1 u
Change	- 1 p	- 3 p
After	120	0

¹₆ = ³₁₈

Cutting the slices of pizzas into same size. Each pizza was cut into 18 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.

Number of slices that the girls had left
= 6²₃ ÷ ¹₁₈ 
= ²⁰₃ x 18
= 120

3 u - 1 p = 120 --- (1)

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

Make u the same.

(2)_x3
3 u = 9 p --- (3)

Substitute (3) into (1).
3 u - 1 p = 120
9 p - 1 p = 120
8 p = 120

1 p = 120 ÷ 8 = 15

Total number of slices of pizzas for girls
= 120 + 1 p
= 120 + 15
= 135

Total number of slices of pizzas for boys
= 135 ÷ 3
= 45

Total number of slices of pizzas for pupils
= 135 + 45
= 180

Total number of pizzas that Mr Paul bought
= 180 ÷ 18
= 10

Answer(s): 10