Mr Gabriel 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
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 6
12 pizzas left. How many pizzas did Mr Gabriel buy?
|
Girls (1) |
Boys (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
39 |
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
= 6
12 ÷
16 =
132 x 6
= 39
2 u - 1 p = 39 --- (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 = 39
4 p - 1 p = 39
3 p = 39
1 p = 39 ÷ 3 = 13
Total number of slices of pizzas for girls
= 39 + 1 p
= 39 + 13
= 52
Total number of slices of pizzas for boys
= 52 ÷ 2
= 26
Total number of slices of pizzas for children
= 52 + 26
= 78
Total number of pizzas that Mr Gabriel bought
= 78 ÷ 6
= 13
Answer(s): 13