There are some green and silver balls in a box. If 4 green balls are removed from the box, the total number of balls left will be 6 times the number of green balls left. If 2 silver balls are removed from the box, the total number of balls left will be 4 times the number of green balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
Green balls |
Silver balls |
Green balls |
Silver balls |
Before |
1 u + 4 |
5 u |
1 p |
3 p + 2 |
Change |
- 4 |
|
|
- 2 |
After |
1 u |
5 u |
1 p |
3 p |
Number of silver balls in the end for Case 1
= 6 u - 1 u
= 5 u
Number of green balls in the end for Case 2
= 4 p - 1 p
= 3 p
The number of green balls at first is the same for Case 1 and Case 2.
The number of silver balls at first is also the same for Case 1 and Case 2.
1 u + 4 = 1 p --- (1)
5 u = 3 p + 2
5 u - 2 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 12 =
3 p --- (3)
(2) = (3)
5 u - 2 = 3 u + 12
5 u - 3 u = 12 + 2
2 u = 14
1 u = 14 ÷ 2 = 7
Number of balls in the box
= (1 u + 4) + 5 u
= 6 u + 4
= (6 x 7) + 4
= 42 + 4
= 46
Answer(s): 46