Mr Glen bought some pizzas for a group of students. There was an equal number of girls and boys. The girls received 2 times as many pizzas as the boys. Each boy ate
16 of a pizza and the boys finished all the pizzas given to them. Each girl ate
112 of a pizza and the girls had 10
12 pizzas left. How many pizzas did Mr Glen buy?
|
Girls (1) |
Boys (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
126 |
0 |
16 =
212 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 2 slices of pizza.
Number of slices that the girls had left
= 10
12 ÷
112 =
212 x 12
= 126
2 u - 1 p = 126 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x22 u = 4 p --- (3)
Substitute (3) into (1).
2 u - 1 p = 126
4 p - 1 p = 126
3 p = 126
1 p = 126 ÷ 3 = 42
Total number of slices of pizzas for girls
= 126 + 1 p
= 126 + 42
= 168
Total number of slices of pizzas for boys
= 168 ÷ 2
= 84
Total number of slices of pizzas for students
= 168 + 84
= 252
Total number of pizzas that Mr Glen bought
= 252 ÷ 12
= 21
Answer(s): 21