Mr Peter bought some pizzas for a group of children. There was an equal number of boys and girls. The boys received 4 times as many pizzas as the girls. Each girl ate
14 of a pizza and the girls finished all the pizzas given to them. Each boy ate
18 of a pizza and the boys had 10
12 pizzas left. How many pizzas did Mr Peter buy?
|
Boys (1) |
Girls (2) |
Before |
4 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
84 |
0 |
14 =
28 Cutting the slices of pizzas into same size. Each pizza was cut into 8 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.
Number of slices that the boys had left
= 10
12 ÷
18 =
212 x 8
= 84
4 u - 1 p = 84 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x44 u = 8 p --- (3)
Substitute (3) into (1).
4 u - 1 p = 84
8 p - 1 p = 84
7 p = 84
1 p = 84 ÷ 7 = 12
Total number of slices of pizzas for boys
= 84 + 1 p
= 84 + 12
= 96
Total number of slices of pizzas for girls
= 96 ÷ 4
= 24
Total number of slices of pizzas for children
= 96 + 24
= 120
Total number of pizzas that Mr Peter bought
= 120 ÷ 8
= 15
Answer(s): 15