There are some grey and silver balls in a box. If 4 grey balls are removed from the box, the total number of balls left will be 9 times the number of grey balls left. If 20 silver balls are removed from the box, the total number of balls left will be 5 times the number of grey balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
Grey balls |
Silver balls |
Grey balls |
Silver balls |
Before |
1 u + 4 |
8 u |
1 p |
4 p + 20 |
Change |
- 4 |
|
|
- 20 |
After |
1 u |
8 u |
1 p |
4 p |
Number of silver balls in the end for Case 1
= 9 u - 1 u
= 8 u
Number of grey balls in the end for Case 2
= 5 p - 1 p
= 4 p
The number of grey 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)
8 u = 4 p + 20
8 u - 20 =
4 p --- (2)
Make p the same.
(1)
x4 4 u + 16 =
4 p --- (3)
(2) = (3)
8 u - 20 = 4 u + 16
8 u - 4 u = 16 + 20
4 u = 36
1 u = 36 ÷ 4 = 9
Number of balls in the box
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 9) + 4
= 81 + 4
= 85
Answer(s): 85