Mr Perry bought some pizzas for a group of students. There was an equal number of girls and boys. The girls received 3 times as many pizzas as the boys. Each boy ate
12 of a pizza and the boys finished all the pizzas given to them. Each girl ate
14 of a pizza and the girls had 7
12 pizzas left. How many pizzas did Mr Perry buy?
| |
Girls
(1) |
Boys
(2) |
| Before |
3 u |
1 u |
| Change |
- 1 p |
- 2 p |
| After |
30 |
0 |
12 =
24 Cutting the slices of pizzas into same size. Each pizza was cut into 4 slices. Every girl ate 1 slice of pizza and every boy ate 2 slices of pizza.
Number of slices that the girls had left
= 7
12 ÷
14 =
152 x 4
= 30
3 u - 1 p = 30 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x33 u = 6 p --- (3)
Substitute (3) into (1).
3 u - 1 p = 30
6 p - 1 p = 30
5 p = 30
1 p = 30 ÷ 5 = 6
Total number of slices of pizzas for girls
= 30 + 1 p
= 30 + 6
= 36
Total number of slices of pizzas for boys
= 36 ÷ 3
= 12
Total number of slices of pizzas for students
= 36 + 12
= 48
Total number of pizzas that Mr Perry bought
= 48 ÷ 4
= 12
Answer(s): 12
