There are some green and brown balls in a box. If 2 green balls are removed from the box, the total number of balls left will be 9 times the number of green balls left. If 4 brown 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 |
Brown balls |
Green balls |
Brown balls |
Before |
1 u + 2 |
8 u |
1 p |
3 p + 4 |
Change |
- 2 |
|
|
- 4 |
After |
1 u |
8 u |
1 p |
3 p |
Number of brown balls in the end for Case 1
= 9 u - 1 u
= 8 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 brown balls at first is also the same for Case 1 and Case 2.
1 u + 2 = 1 p --- (1)
8 u = 3 p + 4
8 u - 4 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 6 =
3 p --- (3)
(2) = (3)
8 u - 4 = 3 u + 6
8 u - 3 u = 6 + 4
5 u = 10
1 u = 10 ÷ 5 = 2
Number of balls in the box
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 2) + 2
= 18 + 2
= 20
Answer(s): 20