Mr Henry bought some pizzas for a group of children. There was an equal number of girls and boys. The girls received 2 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 10
12 pizzas left. How many pizzas did Mr Henry buy?
|
Girls (1) |
Boys (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
42 |
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
= 10
12 ÷
14 =
212 x 4
= 42
2 u - 1 p = 42 --- (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 = 42
4 p - 1 p = 42
3 p = 42
1 p = 42 ÷ 3 = 14
Total number of slices of pizzas for girls
= 42 + 1 p
= 42 + 14
= 56
Total number of slices of pizzas for boys
= 56 ÷ 2
= 28
Total number of slices of pizzas for children
= 56 + 28
= 84
Total number of pizzas that Mr Henry bought
= 84 ÷ 4
= 21
Answer(s): 21