There are some pink and grey balls in a box. If 3 pink balls are removed from the box, the total number of balls left will be 7 times the number of pink balls left. If 3 grey balls are removed from the box, the total number of balls left will be 4 times the number of pink balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
Pink balls |
Grey balls |
Pink balls |
Grey balls |
Before |
1 u + 3 |
6 u |
1 p |
3 p + 3 |
Change |
- 3 |
|
|
- 3 |
After |
1 u |
6 u |
1 p |
3 p |
Number of grey balls in the end for Case 1
= 7 u - 1 u
= 6 u
Number of pink balls in the end for Case 2
= 4 p - 1 p
= 3 p
The number of pink balls at first is the same for Case 1 and Case 2.
The number of grey balls at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
6 u = 3 p + 3
6 u - 3 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 9 =
3 p --- (3)
(2) = (3)
6 u - 3 = 3 u + 9
6 u - 3 u = 9 + 3
3 u = 12
1 u = 12 ÷ 3 = 4
Number of balls in the box
= (1 u + 3) + 6 u
= 7 u + 3
= (7 x 4) + 3
= 28 + 3
= 31
Answer(s): 31