Mr Peter bought some pizzas for a group of students. There was an equal number of boys and girls. The boys received 3 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
16 of a pizza and the boys had 7
12 pizzas left. How many pizzas did Mr Peter buy?
| |
Boys
(1) |
Girls
(2) |
| Before |
3 u |
1 u |
| Change |
- 1 p |
- 2 p |
| After |
45 |
0 |
13 =
26 Cutting the slices of pizzas into same size. Each pizza was cut into 6 slices. Every boy ate 1 slice of pizza and every girl ate 2 slices of pizza.
Number of slices that the boys had left
= 7
12 ÷
16 =
152 x 6
= 45
3 u - 1 p = 45 --- (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 = 45
6 p - 1 p = 45
5 p = 45
1 p = 45 ÷ 5 = 9
Total number of slices of pizzas for boys
= 45 + 1 p
= 45 + 9
= 54
Total number of slices of pizzas for girls
= 54 ÷ 3
= 18
Total number of slices of pizzas for students
= 54 + 18
= 72
Total number of pizzas that Mr Peter bought
= 72 ÷ 6
= 12
Answer(s): 12
