There are some white and yellow balls in a box. If 3 white balls are removed from the box, the total number of balls left will be 4 times the number of white balls left. If 4 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 + 3 |
3 u |
1 p |
2 p + 4 |
Change |
- 3 |
|
|
- 4 |
After |
1 u |
3 u |
1 p |
2 p |
Number of yellow balls in the end for Case 1
= 4 u - 1 u
= 3 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 + 3 = 1 p --- (1)
3 u = 2 p + 4
3 u - 4 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 6 =
2 p --- (3)
(2) = (3)
3 u - 4 = 2 u + 6
3 u - 2 u = 6 + 4
1 u = 10
1 u = 10 ÷ 1 = 10
Number of balls in the box
= (1 u + 3) + 3 u
= 4 u + 3
= (4 x 10) + 3
= 40 + 3
= 43
Answer(s): 43