Mr Billy bought some pizzas for a group of children. There was an equal number of girls and boys. The girls received 5 times as many pizzas as the boys. Each boy ate
12 of a pizza and the boys finished all the pizzas given to them. Each girl ate
14 of a pizza and the girls had 13
12 pizzas left. How many pizzas did Mr Billy buy?
|
Girls (1) |
Boys (2) |
Before |
5 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
54 |
0 |
12 =
24 Cutting the slices of pizzas into same size. Each pizza was cut into 4 slices. Every girl ate 1 slice of pizza and every boy ate 2 slices of pizza.
Number of slices that the girls had left
= 13
12 ÷
14 =
272 x 4
= 54
5 u - 1 p = 54 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x55 u = 10 p --- (3)
Substitute (3) into (1).
5 u - 1 p = 54
10 p - 1 p = 54
9 p = 54
1 p = 54 ÷ 9 = 6
Total number of slices of pizzas for girls
= 54 + 1 p
= 54 + 6
= 60
Total number of slices of pizzas for boys
= 60 ÷ 5
= 12
Total number of slices of pizzas for children
= 60 + 12
= 72
Total number of pizzas that Mr Billy bought
= 72 ÷ 4
= 18
Answer(s): 18