Mr Andy bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 5 times as many pizzas as the boys. Each boy ate
14 of a pizza and the boys finished all the pizzas given to them. Each girl ate
112 of a pizza and the girls had 11
23 pizzas left. How many pizzas did Mr Andy buy?
|
Girls (1) |
Boys (2) |
Before |
5 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
140 |
0 |
14 =
312 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 3 slices of pizza.
Number of slices that the girls had left
= 11
23 ÷
112 =
353 x 12
= 140
5 u - 1 p = 140 --- (1)
1 u - 3 p = 0
1 u = 3 p --- (2)
Make u the same.
(2)
x55 u = 15 p --- (3)
Substitute (3) into (1).
5 u - 1 p = 140
15 p - 1 p = 140
14 p = 140
1 p = 140 ÷ 14 = 10
Total number of slices of pizzas for girls
= 140 + 1 p
= 140 + 10
= 150
Total number of slices of pizzas for boys
= 150 ÷ 5
= 30
Total number of slices of pizzas for pupils
= 150 + 30
= 180
Total number of pizzas that Mr Andy bought
= 180 ÷ 12
= 15
Answer(s): 15