Mr Liam bought some pizzas for a group of children. There was an equal number of boys and girls. The boys received 2 times as many pizzas as the girls. Each girl ate
12 of a pizza and the girls finished all the pizzas given to them. Each boy ate
14 of a pizza and the boys had 7
12 pizzas left. How many pizzas did Mr Liam buy?
|
Boys (1) |
Girls (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
30 |
0 |
12 =
24 Cutting the slices of pizzas into same size. Each pizza was cut into 4 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.
Number of slices that the boys had left
= 7
12 ÷
14 =
152 x 4
= 30
2 u - 1 p = 30 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x22 u = 4 p --- (3)
Substitute (3) into (1).
2 u - 1 p = 30
4 p - 1 p = 30
3 p = 30
1 p = 30 ÷ 3 = 10
Total number of slices of pizzas for boys
= 30 + 1 p
= 30 + 10
= 40
Total number of slices of pizzas for girls
= 40 ÷ 2
= 20
Total number of slices of pizzas for children
= 40 + 20
= 60
Total number of pizzas that Mr Liam bought
= 60 ÷ 4
= 15
Answer(s): 15