Mr Jack 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 ¹₃ of a pizza and the boys finished all the pizzas given to them. Each girl ate ¹₉ of a pizza and the girls had 5¹₃ pizzas left. How many pizzas did Mr Jack buy?

	Girls (1)	Boys (2)
Before	3 u	1 u
Change	- 1 p	- 3 p
After	48	0

¹₃ = ³₉

Cutting the slices of pizzas into same size. Each pizza was cut into 9 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.

Number of slices that the girls had left
= 5¹₃ ÷ ¹₉ 
= ¹⁶₃ x 9
= 48

3 u - 1 p = 48 --- (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 = 48
9 p - 1 p = 48
8 p = 48

1 p = 48 ÷ 8 = 6

Total number of slices of pizzas for girls
= 48 + 1 p
= 48 + 6
= 54

Total number of slices of pizzas for boys
= 54 ÷ 3
= 18

Total number of slices of pizzas for students
= 54 + 18
= 72

Total number of pizzas that Mr Jack bought
= 72 ÷ 9
= 8

Answer(s): 8