Mr Julian bought some pizzas for a group of pupils. There was an equal number of boys and girls. The boys received 3 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 ¹₁₈ of a pizza and the boys had 13¹₃ pizzas left. How many pizzas did Mr Julian buy?

	Boys (1)	Girls (2)
Before	3 u	1 u
Change	- 1 p	- 3 p
After	240	0

¹₆ = ³₁₈

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

Number of slices that the boys had left
= 13¹₃ ÷ ¹₁₈ 
= ⁴⁰₃ x 18
= 240

3 u - 1 p = 240 --- (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 = 240
9 p - 1 p = 240
8 p = 240

1 p = 240 ÷ 8 = 30

Total number of slices of pizzas for boys
= 240 + 1 p
= 240 + 30
= 270

Total number of slices of pizzas for girls
= 270 ÷ 3
= 90

Total number of slices of pizzas for pupils
= 270 + 90
= 360

Total number of pizzas that Mr Julian bought
= 360 ÷ 18
= 20

Answer(s): 20