Mr Tom bought some pizzas for a group of pupils. There was an equal number of boys and girls. The boys received 2 times as many pizzas as the girls. Each girl ate
13 of a pizza and the girls finished all the pizzas given to them. Each boy ate
19 of a pizza and the boys had 8
13 pizzas left. How many pizzas did Mr Tom buy?
|
Boys (1) |
Girls (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
75 |
0 |
13 =
39 Cutting the slices of pizzas into same size. Each pizza was cut into 9 slices. Every boy ate 1 slice of pizza and every girl ate 3 slices of pizza.
Number of slices that the boys had left
= 8
13 ÷
19 =
253 x 9
= 75
2 u - 1 p = 75 --- (1)
1 u - 3 p = 0
1 u = 3 p --- (2)
Make u the same.
(2)
x22 u = 6 p --- (3)
Substitute (3) into (1).
2 u - 1 p = 75
6 p - 1 p = 75
5 p = 75
1 p = 75 ÷ 5 = 15
Total number of slices of pizzas for boys
= 75 + 1 p
= 75 + 15
= 90
Total number of slices of pizzas for girls
= 90 ÷ 2
= 45
Total number of slices of pizzas for pupils
= 90 + 45
= 135
Total number of pizzas that Mr Tom bought
= 135 ÷ 9
= 15
Answer(s): 15