Mr Simon bought some pizzas for a group of students. 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
112 of a pizza and the boys had 7
13 pizzas left. How many pizzas did Mr Simon buy?
|
Boys (1) |
Girls (2) |
Before |
4 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
88 |
0 |
14 =
312 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 3 slices of pizza.
Number of slices that the boys had left
= 7
13 ÷
112 =
223 x 12
= 88
4 u - 1 p = 88 --- (1)
1 u - 3 p = 0
1 u = 3 p --- (2)
Make u the same.
(2)
x44 u = 12 p --- (3)
Substitute (3) into (1).
4 u - 1 p = 88
12 p - 1 p = 88
11 p = 88
1 p = 88 ÷ 11 = 8
Total number of slices of pizzas for boys
= 88 + 1 p
= 88 + 8
= 96
Total number of slices of pizzas for girls
= 96 ÷ 4
= 24
Total number of slices of pizzas for students
= 96 + 24
= 120
Total number of pizzas that Mr Simon bought
= 120 ÷ 12
= 10
Answer(s): 10