Mr Luke bought some pizzas for a group of students. There was an equal number of boys and girls. The boys received 2 times as many pizzas as the girls. Each girl ate ¹₃ of a pizza and the girls finished all the pizzas given to them. Each boy ate ¹₆ of a pizza and the boys had 14¹₂ pizzas left. How many pizzas did Mr Luke buy?

	Boys (1)	Girls (2)
Before	2 u	1 u
Change	- 1 p	- 2 p
After	87	0

¹₃ = ²₆

Cutting the slices of pizzas into same size. Each pizza was cut into 6 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.

Number of slices that the boys had left
= 14¹₂ ÷ ¹₆ 
= ²⁹₂ x 6
= 87

2 u - 1 p = 87 --- (1)

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

Make u the same.

(2)_x2
2 u = 4 p --- (3)

Substitute (3) into (1).
2 u - 1 p = 87
4 p - 1 p = 87
3 p = 87

1 p = 87 ÷ 3 = 29

Total number of slices of pizzas for boys
= 87 + 1 p
= 87 + 29
= 116

Total number of slices of pizzas for girls
= 116 ÷ 2
= 58

Total number of slices of pizzas for students
= 116 + 58
= 174

Total number of pizzas that Mr Luke bought
= 174 ÷ 6
= 29

Answer(s): 29