Crate R contains 8 brown balls and 4 green balls. Crate S contains 38 brown balls and 20 green balls. How many green balls and brown balls must be removed from Crate S to put into Crate R so that 50% of the balls in Crate A are brown and 75% of the balls in Crate S are brown?
|
Crate R |
Crate S |
|
Brown balls |
Green balls |
Brown balls |
Green balls |
Before |
8 |
4 |
38 |
20 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of brown balls = 8 + 38 = 46
Number of green balls = 4 + 20 = 24
1 u + 3 p = 46 --- (1)
1 u + 1 p = 24 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 46 - 24
3 p - 1 p = 22
2 p = 22
1 p = 22 ÷ 2 = 11
From (2):
1 u + 1 p = 24
1 u + 1 x 11 = 24
1 u + 11 = 24
1 u = 24 - 11 = 13
Number of green balls to be removed from Crate S to Crate R
= 20 - 1 p
= 20 - 1 x 11
= 20 - 11
= 9
Number of brown balls to be removed from Crate S to Crate R
= 1 u - 8
= 13 - 8
= 5
Total number of green and brown balls to be removed from Crate S to Crate R
= 9 + 5
= 14
Answer(s): 14