Mr Charlie bought some pizzas for a group of children. There was an equal number of boys and girls. The boys received 3 times as many pizzas as the girls. Each girl ate
15 of a pizza and the girls finished all the pizzas given to them. Each boy ate
115 of a pizza and the boys had 5
13 pizzas left. How many pizzas did Mr Charlie buy?
|
Boys (1) |
Girls (2) |
Before |
3 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
80 |
0 |
15 =
315 Cutting the slices of pizzas into same size. Each pizza was cut into 15 slices. Every boy ate 1 slice of pizza and every girl ate 3 slices of pizza.
Number of slices that the boys had left
= 5
13 ÷
115 =
163 x 15
= 80
3 u - 1 p = 80 --- (1)
1 u - 3 p = 0
1 u = 3 p --- (2)
Make u the same.
(2)
x33 u = 9 p --- (3)
Substitute (3) into (1).
3 u - 1 p = 80
9 p - 1 p = 80
8 p = 80
1 p = 80 ÷ 8 = 10
Total number of slices of pizzas for boys
= 80 + 1 p
= 80 + 10
= 90
Total number of slices of pizzas for girls
= 90 ÷ 3
= 30
Total number of slices of pizzas for children
= 90 + 30
= 120
Total number of pizzas that Mr Charlie bought
= 120 ÷ 15
= 8
Answer(s): 8