There are some white and yellow balls in a box. If 4 white balls are removed from the box, the total number of balls left will be 7 times the number of white balls left. If 16 yellow balls are removed from the box, the total number of balls left will be 3 times the number of white balls. How many balls are there in the box?
|
Case 1 |
Case 2 |
|
White balls |
Yellow balls |
White balls |
Yellow balls |
Before |
1 u + 4 |
6 u |
1 p |
2 p + 16 |
Change |
- 4 |
|
|
- 16 |
After |
1 u |
6 u |
1 p |
2 p |
Number of yellow balls in the end for Case 1
= 7 u - 1 u
= 6 u
Number of white balls in the end for Case 2
= 3 p - 1 p
= 2 p
The number of white balls at first is the same for Case 1 and Case 2.
The number of yellow balls at first is also the same for Case 1 and Case 2.
1 u + 4 = 1 p --- (1)
6 u = 2 p + 16
6 u - 16 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 8 =
2 p --- (3)
(2) = (3)
6 u - 16 = 2 u + 8
6 u - 2 u = 8 + 16
4 u = 24
1 u = 24 ÷ 4 = 6
Number of balls in the box
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 6) + 4
= 42 + 4
= 46
Answer(s): 46