Mr Owen bought some pizzas for a group of children. There was an equal number of boys and girls. The boys received 3 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
118 of a pizza and the boys had 14
23 pizzas left. How many pizzas did Mr Owen buy?
|
Boys (1) |
Girls (2) |
Before |
3 u |
1 u |
Change |
- 1 p |
- 3 p |
After |
264 |
0 |
16 =
318 Cutting the slices of pizzas into same size. Each pizza was cut into 18 slices. Every boy ate 1 slice of pizza and every girl ate 3 slices of pizza.
Number of slices that the boys had left
= 14
23 ÷
118 =
443 x 18
= 264
3 u - 1 p = 264 --- (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 = 264
9 p - 1 p = 264
8 p = 264
1 p = 264 ÷ 8 = 33
Total number of slices of pizzas for boys
= 264 + 1 p
= 264 + 33
= 297
Total number of slices of pizzas for girls
= 297 ÷ 3
= 99
Total number of slices of pizzas for children
= 297 + 99
= 396
Total number of pizzas that Mr Owen bought
= 396 ÷ 18
= 22
Answer(s): 22