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
118 of a pizza and the girls had 10
59 pizzas left. How many pizzas did Mr Valen buy?
|
Girls (1) |
Boys (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
190 |
0 |
16 =
318 Cutting the slices of pizzas into same size. Each pizza was cut into 18 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.
Number of slices that the girls had left
= 10
59 ÷
118 =
959 x 18
= 190
2 u - 1 p = 190 --- (1)
1 u - 3 p = 0
1 u = 3 p --- (2)
Make u the same.
(2)
x22 u = 6 p --- (3)
Substitute (3) into (1).
2 u - 1 p = 190
6 p - 1 p = 190
5 p = 190
1 p = 190 ÷ 5 = 38
Total number of slices of pizzas for girls
= 190 + 1 p
= 190 + 38
= 228
Total number of slices of pizzas for boys
= 228 ÷ 2
= 114
Total number of slices of pizzas for pupils
= 228 + 114
= 342
Total number of pizzas that Mr Valen bought
= 342 ÷ 18
= 19
Answer(s): 19