Mr Peter bought some pizzas for a group of children. There was an equal number of boys and girls. The boys received 5 times as many pizzas as the girls. Each girl ate
16 of a pizza and the girls finished all the pizzas given to them. Each boy ate
112 of a pizza and the boys had 5
14 pizzas left. How many pizzas did Mr Peter buy?
| |
Boys
(1) |
Girls
(2) |
| Before |
5 u |
1 u |
| Change |
- 1 p |
- 2 p |
| After |
63 |
0 |
16 =
212 Cutting the slices of pizzas into same size. Each pizza was cut into 12 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.
Number of slices that the boys had left
= 5
14 ÷
112 =
214 x 12
= 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 boys
= 63 + 1 p
= 63 + 7
= 70
Total number of slices of pizzas for girls
= 70 ÷ 5
= 14
Total number of slices of pizzas for children
= 70 + 14
= 84
Total number of pizzas that Mr Peter bought
= 84 ÷ 12
= 7
Answer(s): 7
