Mr Sam bought some pizzas for a group of students. There was an equal number of boys and girls. The boys received 3 times as many pizzas as the girls. Each girl ate ¹₂ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₄ of a pizza and the boys had 7¹₂ pizzas left. How many pizzas did Mr Sam buy?

	Boys (1)	Girls (2)
Before	3 u	1 u
Change	- 1 p	- 2 p
After	30	0

¹₂ = ²₄

Cutting the slices of pizzas into same size. Each pizza was cut into 4 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.

Number of slices that the boys had left
= 7¹₂ ÷ ¹₄ 
= ¹⁵₂ x 4
= 30

3 u - 1 p = 30 --- (1)

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

Make u the same.

(2)_x3
3 u = 6 p --- (3)

Substitute (3) into (1).
3 u - 1 p = 30
6 p - 1 p = 30
5 p = 30

1 p = 30 ÷ 5 = 6

Total number of slices of pizzas for boys
= 30 + 1 p
= 30 + 6
= 36

Total number of slices of pizzas for girls
= 36 ÷ 3
= 12

Total number of slices of pizzas for students
= 36 + 12
= 48

Total number of pizzas that Mr Sam bought
= 48 ÷ 4
= 12

Answer(s): 12