There are some green and grey balls in a box. If 5 green balls are removed from the box, the total number of balls left will be 4 times the number of green balls left. If 2 grey balls are removed from the box, the total number of balls left will be 3 times the number of green balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
Green balls |
Grey balls |
Green balls |
Grey balls |
Before |
1 u + 5 |
3 u |
1 p |
2 p + 2 |
Change |
- 5 |
|
|
- 2 |
After |
1 u |
3 u |
1 p |
2 p |
Number of grey balls in the end for Case 1
= 4 u - 1 u
= 3 u
Number of green balls in the end for Case 2
= 3 p - 1 p
= 2 p
The number of green balls at first is the same for Case 1 and Case 2.
The number of grey balls at first is also the same for Case 1 and Case 2.
1 u + 5 = 1 p --- (1)
3 u = 2 p + 2
3 u - 2 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 10 =
2 p --- (3)
(2) = (3)
3 u - 2 = 2 u + 10
3 u - 2 u = 10 + 2
1 u = 12
1 u = 12 ÷ 1 = 12
Number of balls in the box
= (1 u + 5) + 3 u
= 4 u + 5
= (4 x 12) + 5
= 48 + 5
= 53
Answer(s): 53