There are some green and gold balls in a container. If 4 green balls are removed from the container, the total number of balls left will be 9 times the number of green balls left. If 16 gold balls are removed from the container, the total number of balls left will be 6 times the number of green balls. How many balls are there in the container?
|
Case 1 |
Case 2 |
|
Green balls |
Gold balls |
Green balls |
Gold balls |
Before |
1 u + 4 |
8 u |
1 p |
5 p + 16 |
Change |
- 4 |
|
|
- 16 |
After |
1 u |
8 u |
1 p |
5 p |
Number of gold balls in the end for Case 1
= 9 u - 1 u
= 8 u
Number of green balls in the end for Case 2
= 6 p - 1 p
= 5 p
The number of green balls at first is the same for Case 1 and Case 2.
The number of gold balls at first is also the same for Case 1 and Case 2.
1 u + 4 = 1 p --- (1)
8 u = 5 p + 16
8 u - 16 =
5 p --- (2)
Make p the same.
(1)
x5 5 u + 20 =
5 p --- (3)
(2) = (3)
8 u - 16 = 5 u + 20
8 u - 5 u = 20 + 16
3 u = 36
1 u = 36 ÷ 3 = 12
Number of balls in the container
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 12) + 4
= 108 + 4
= 112
Answer(s): 112