Mr Xavier 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
13 of a pizza and the boys finished all the pizzas given to them. Each girl ate
16 of a pizza and the girls had 10
12 pizzas left. How many pizzas did Mr Xavier buy?
|
Girls (1) |
Boys (2) |
Before |
5 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
63 |
0 |
13 =
26 Cutting the slices of pizzas into same size. Each pizza was cut into 6 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 ÷
16 =
212 x 6
= 63
5 u - 1 p = 63 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x55 u = 10 p --- (3)
Substitute (3) into (1).
5 u - 1 p = 63
10 p - 1 p = 63
9 p = 63
1 p = 63 ÷ 9 = 7
Total number of slices of pizzas for girls
= 63 + 1 p
= 63 + 7
= 70
Total number of slices of pizzas for boys
= 70 ÷ 5
= 14
Total number of slices of pizzas for pupils
= 70 + 14
= 84
Total number of pizzas that Mr Xavier bought
= 84 ÷ 6
= 14
Answer(s): 14