Mr Zane 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
14 of a pizza and the boys finished all the pizzas given to them. Each girl ate
112 of a pizza and the girls had 5
13 pizzas left. How many pizzas did Mr Zane buy?
|
Girls (1) |
Boys (2) |
Before |
3 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
64 |
0 |
14 =
312 Cutting the slices of pizzas into same size. Each pizza was cut into 12 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.
Number of slices that the girls had left
= 5
13 ÷
112 =
163 x 12
= 64
3 u - 1 p = 64 --- (1)
1 u - 3 p = 0
1 u = 3 p --- (2)
Make u the same.
(2)
x33 u = 9 p --- (3)
Substitute (3) into (1).
3 u - 1 p = 64
9 p - 1 p = 64
8 p = 64
1 p = 64 ÷ 8 = 8
Total number of slices of pizzas for girls
= 64 + 1 p
= 64 + 8
= 72
Total number of slices of pizzas for boys
= 72 ÷ 3
= 24
Total number of slices of pizzas for students
= 72 + 24
= 96
Total number of pizzas that Mr Zane bought
= 96 ÷ 12
= 8
Answer(s): 8