Mr Xavier bought some pizzas for a group of students. There was an equal number of girls and boys. The girls received 2 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 12²₉ pizzas left. How many pizzas did Mr Xavier buy?

	Girls (1)	Boys (2)
Before	2 u	1 u
Change	- 1 p	- 3 p
After	220	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
= 12²₉ ÷ ¹₁₈ 
= ¹¹⁰₉ x 18
= 220

2 u - 1 p = 220 --- (1)

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

Make u the same.

(2)_x2
2 u = 6 p --- (3)

Substitute (3) into (1).
2 u - 1 p = 220
6 p - 1 p = 220
5 p = 220

1 p = 220 ÷ 5 = 44

Total number of slices of pizzas for girls
= 220 + 1 p
= 220 + 44
= 264

Total number of slices of pizzas for boys
= 264 ÷ 2
= 132

Total number of slices of pizzas for students
= 264 + 132
= 396

Total number of pizzas that Mr Xavier bought
= 396 ÷ 18
= 22

Answer(s): 22