There are some purple and silver balls in a container. If 2 purple balls are removed from the container, the total number of balls left will be 9 times the number of purple balls left. If 8 silver balls are removed from the container, the total number of balls left will be 3 times the number of purple balls. How many balls are there in the container?
|
Case 1 |
Case 2 |
|
Purple balls |
Silver balls |
Purple balls |
Silver balls |
Before |
1 u + 2 |
8 u |
1 p |
2 p + 8 |
Change |
- 2 |
|
|
- 8 |
After |
1 u |
8 u |
1 p |
2 p |
Number of silver balls in the end for Case 1
= 9 u - 1 u
= 8 u
Number of purple balls in the end for Case 2
= 3 p - 1 p
= 2 p
The number of purple 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 + 2 = 1 p --- (1)
8 u = 2 p + 8
8 u - 8 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 4 =
2 p --- (3)
(2) = (3)
8 u - 8 = 2 u + 4
8 u - 2 u = 4 + 8
6 u = 12
1 u = 12 ÷ 6 = 2
Number of balls in the container
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 2) + 2
= 18 + 2
= 20
Answer(s): 20