Box S contains 7 silver balls and 6 green balls. Box T contains 55 silver balls and 28 green balls. How many green balls and silver balls must be removed from Box T to put into Box S so that 50% of the balls in Box A are silver and 70% of the balls in Box T are silver?
|
Box S |
Box T |
|
Silver balls |
Green balls |
Silver balls |
Green balls |
Before |
7 |
6 |
55 |
28 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
7 p |
3 p |
50% =
50100 = 12
70% =
70100 = 710
Number of silver balls = 7 + 55 = 62
Number of green balls = 6 + 28 = 34
1 u + 7 p = 62 --- (1)
1 u + 3 p = 34 ---(2)
(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 62 - 34
7 p - 3 p = 28
4 p = 28
1 p = 28 ÷ 4 = 7
From (2):
1 u + 3 p = 34
1 u + 3 x 7 = 34
1 u + 21 = 34
1 u = 34 - 21 = 13
Number of green balls to be removed from Box T to Box S
= 28 - 3 p
= 28 - 3 x 7
= 28 - 21
= 7
Number of silver balls to be removed from Box T to Box S
= 1 u - 7
= 13 - 7
= 6
Total number of green and silver balls to be removed from Box T to Box S
= 7 + 6
= 13
Answer(s): 13