Mr Zane bought some pizzas for a group of pupils. There was an equal number of girls and boys. The girls received 3 times as many pizzas as the boys. Each boy ate
13 of a pizza and the boys finished all the pizzas given to them. Each girl ate
16 of a pizza and the girls had 12
12 pizzas left. How many pizzas did Mr Zane buy?
|
Girls (1) |
Boys (2) |
Before |
3 u |
1 u |
Change |
- 1 p |
- 2 p |
After |
75 |
0 |
13 =
26 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 2 slices of pizza.
Number of slices that the girls had left
= 12
12 ÷
16 =
252 x 6
= 75
3 u - 1 p = 75 --- (1)
1 u - 2 p = 0
1 u = 2 p --- (2)
Make u the same.
(2)
x33 u = 6 p --- (3)
Substitute (3) into (1).
3 u - 1 p = 75
6 p - 1 p = 75
5 p = 75
1 p = 75 ÷ 5 = 15
Total number of slices of pizzas for girls
= 75 + 1 p
= 75 + 15
= 90
Total number of slices of pizzas for boys
= 90 ÷ 3
= 30
Total number of slices of pizzas for pupils
= 90 + 30
= 120
Total number of pizzas that Mr Zane bought
= 120 ÷ 6
= 20
Answer(s): 20