Mr Owen bought some pizzas for a group of students. There was an equal number of boys and girls. The boys received 2 times as many pizzas as the girls. Each girl ate
15 of a pizza and the girls finished all the pizzas given to them. Each boy ate
115 of a pizza and the boys had 6
23 pizzas left. How many pizzas did Mr Owen buy?
|
Boys (1) |
Girls (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
100 |
0 |
15 =
315 Cutting the slices of pizzas into same size. Each pizza was cut into 15 slices. Every boy ate 1 slice of pizza and every girl ate 3 slices of pizza.
Number of slices that the boys had left
= 6
23 ÷
115 =
203 x 15
= 100
2 u - 1 p = 100 --- (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 = 100
6 p - 1 p = 100
5 p = 100
1 p = 100 ÷ 5 = 20
Total number of slices of pizzas for boys
= 100 + 1 p
= 100 + 20
= 120
Total number of slices of pizzas for girls
= 120 ÷ 2
= 60
Total number of slices of pizzas for students
= 120 + 60
= 180
Total number of pizzas that Mr Owen bought
= 180 ÷ 15
= 12
Answer(s): 12