Mr Andy 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
12 of a pizza and the boys finished all the pizzas given to them. Each girl ate
16 of a pizza and the girls had 14
23 pizzas left. How many pizzas did Mr Andy buy?
| |
Girls
(1) |
Boys
(2) |
| Before |
3 u |
1 u |
| Change |
- 1 p |
- 3 p |
| After |
88 |
0 |
12 =
36 Cutting the slices of pizzas into same size. Each pizza was cut into 6 slices. Every girl ate 1 slice of pizza and every boy ate 3 slices of pizza.
Number of slices that the girls had left
= 14
23 ÷
16 =
443 x 6
= 88
3 u - 1 p = 88 --- (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 = 88
9 p - 1 p = 88
8 p = 88
1 p = 88 ÷ 8 = 11
Total number of slices of pizzas for girls
= 88 + 1 p
= 88 + 11
= 99
Total number of slices of pizzas for boys
= 99 ÷ 3
= 33
Total number of slices of pizzas for students
= 99 + 33
= 132
Total number of pizzas that Mr Andy bought
= 132 ÷ 6
= 22
Answer(s): 22
