Mr Tom bought some pizzas for a group of pupils. 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 6
34 pizzas left. How many pizzas did Mr Tom buy?
|
Boys (1) |
Girls (2) |
Before |
5 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
81 |
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
= 6
34 ÷
112 =
274 x 12
= 81
5 u - 1 p = 81 --- (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 = 81
10 p - 1 p = 81
9 p = 81
1 p = 81 ÷ 9 = 9
Total number of slices of pizzas for boys
= 81 + 1 p
= 81 + 9
= 90
Total number of slices of pizzas for girls
= 90 ÷ 5
= 18
Total number of slices of pizzas for pupils
= 90 + 18
= 108
Total number of pizzas that Mr Tom bought
= 108 ÷ 12
= 9
Answer(s): 9