Mr Asher bought some pizzas for a group of students. There was an equal number of girls and boys. The girls received 3 times as many pizzas as the boys. Each boy ate ¹₄ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₈ of a pizza and the girls had 10⁵₈ pizzas left. How many pizzas did Mr Asher buy?

	Girls (1)	Boys (2)
Before	3 u	1 u
Change	- 1 p	- 2 p
After	85	0

¹₄ = ²₈

Cutting the slices of pizzas into same size. Each pizza was cut into 8 slices. Every girl ate 1 slice of pizza and every boy ate 2 slices of pizza.

Number of slices that the girls had left
= 10⁵₈ ÷ ¹₈ 
= ⁸⁵₈ x 8
= 85

3 u - 1 p = 85 --- (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 = 85
6 p - 1 p = 85
5 p = 85

1 p = 85 ÷ 5 = 17

Total number of slices of pizzas for girls
= 85 + 1 p
= 85 + 17
= 102

Total number of slices of pizzas for boys
= 102 ÷ 3
= 34

Total number of slices of pizzas for students
= 102 + 34
= 136

Total number of pizzas that Mr Asher bought
= 136 ÷ 8
= 17

Answer(s): 17