There are some white and pink balls in a box. If 3 white balls are removed from the box, the total number of balls left will be 9 times the number of white balls left. If 6 pink balls are removed from the box, the total number of balls left will be 6 times the number of white balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
White balls |
Pink balls |
White balls |
Pink balls |
Before |
1 u + 3 |
8 u |
1 p |
5 p + 6 |
Change |
- 3 |
|
|
- 6 |
After |
1 u |
8 u |
1 p |
5 p |
Number of pink balls in the end for Case 1
= 9 u - 1 u
= 8 u
Number of white balls in the end for Case 2
= 6 p - 1 p
= 5 p
The number of white balls at first is the same for Case 1 and Case 2.
The number of pink balls at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
8 u = 5 p + 6
8 u - 6 =
5 p --- (2)
Make p the same.
(1)
x5 5 u + 15 =
5 p --- (3)
(2) = (3)
8 u - 6 = 5 u + 15
8 u - 5 u = 15 + 6
3 u = 21
1 u = 21 ÷ 3 = 7
Number of balls in the box
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 7) + 3
= 63 + 3
= 66
Answer(s): 66