Mr Fabian bought some pizzas for a group of students. There was an equal number of boys and girls. The boys received 2 times as many pizzas as the girls. Each girl ate
16 of a pizza and the girls finished all the pizzas given to them. Each boy ate
112 of a pizza and the boys had 14
12 pizzas left. How many pizzas did Mr Fabian buy?
|
Boys (1) |
Girls (2) |
Before |
2 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
174 |
0 |
16 =
212 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 2 slices of pizza.
Number of slices that the boys had left
= 14
12 ÷
112 =
292 x 12
= 174
2 u - 1 p = 174 --- (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 = 174
4 p - 1 p = 174
3 p = 174
1 p = 174 ÷ 3 = 58
Total number of slices of pizzas for boys
= 174 + 1 p
= 174 + 58
= 232
Total number of slices of pizzas for girls
= 232 ÷ 2
= 116
Total number of slices of pizzas for students
= 232 + 116
= 348
Total number of pizzas that Mr Fabian bought
= 348 ÷ 12
= 29
Answer(s): 29