Mr Valen bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 2 times as many pizzas as the boys. Each boy ate
16 of a pizza and the boys finished all the pizzas given to them. Each girl ate
112 of a pizza and the girls had 8
12 pizzas left. How many pizzas did Mr Valen buy?
| |
Girls
(1) |
Boys
(2) |
| Before |
2 u |
1 u |
| Change |
- 1 p |
- 2 p |
| After |
102 |
0 |
16 =
212 Cutting the slices of pizzas into same size. Each pizza was cut into 12 slices. Every girl ate 1 slice of pizza and every boy ate 2 slices of pizza.
Number of slices that the girls had left
= 8
12 ÷
112 =
172 x 12
= 102
2 u - 1 p = 102 --- (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 = 102
4 p - 1 p = 102
3 p = 102
1 p = 102 ÷ 3 = 34
Total number of slices of pizzas for girls
= 102 + 1 p
= 102 + 34
= 136
Total number of slices of pizzas for boys
= 136 ÷ 2
= 68
Total number of slices of pizzas for pupils
= 136 + 68
= 204
Total number of pizzas that Mr Valen bought
= 204 ÷ 12
= 17
Answer(s): 17
