Mr Charlie 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 ¹₄ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₁₂ of a pizza and the boys had 12²₃ pizzas left. How many pizzas did Mr Charlie buy?

	Boys (1)	Girls (2)
Before	3 u	1 u
Change	- 1 p	- 3 p
After	152	0

¹₄ = ³₁₂

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 3 slices of pizza.

Number of slices that the boys had left
= 12²₃ ÷ ¹₁₂ 
= ³⁸₃ x 12
= 152

3 u - 1 p = 152 --- (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 = 152
9 p - 1 p = 152
8 p = 152

1 p = 152 ÷ 8 = 19

Total number of slices of pizzas for boys
= 152 + 1 p
= 152 + 19
= 171

Total number of slices of pizzas for girls
= 171 ÷ 3
= 57

Total number of slices of pizzas for students
= 171 + 57
= 228

Total number of pizzas that Mr Charlie bought
= 228 ÷ 12
= 19

Answer(s): 19