Crate V contains 15 gold balls and 10 green balls. Crate W contains 36 gold balls and 19 green balls. How many green balls and gold balls must be transferred from Crate W to put into Crate V so that 50% of the balls in Crate A are gold and 75% of the balls in Crate W are gold?
|
Crate V |
Crate W |
|
Gold balls |
Green balls |
Gold balls |
Green balls |
Before |
15 |
10 |
36 |
19 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of gold balls = 15 + 36 = 51
Number of green balls = 10 + 19 = 29
1 u + 3 p = 51 --- (1)
1 u + 1 p = 29 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 51 - 29
3 p - 1 p = 22
2 p = 22
1 p = 22 ÷ 2 = 11
From (2):
1 u + 1 p = 29
1 u + 1 x 11 = 29
1 u + 11 = 29
1 u = 29 - 11 = 18
Number of green balls to be transferred from Crate W to Crate V
= 19 - 1 p
= 19 - 1 x 11
= 19 - 11
= 8
Number of gold balls to be transferred from Crate W to Crate V
= 1 u - 15
= 18 - 15
= 3
Total number of green and gold balls to be transferred from Crate W to Crate V
= 8 + 3
= 11
Answer(s): 11