There are some red and white marbles in a box. If 4 red marbles are removed from the box, the total number of marbles left will be 7 times the number of red marbles left. If 8 white marbles are removed from the box, the total number of marbles left will be 3 times the number of red marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Red marbles |
White marbles |
Red marbles |
White marbles |
Before |
1 u + 4 |
6 u |
1 p |
2 p + 8 |
Change |
- 4 |
|
|
- 8 |
After |
1 u |
6 u |
1 p |
2 p |
Number of white marbles in the end for Case 1
= 7 u - 1 u
= 6 u
Number of red marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of red marbles at first is the same for Case 1 and Case 2.
The number of white marbles at first is also the same for Case 1 and Case 2.
1 u + 4 = 1 p --- (1)
6 u = 2 p + 8
6 u - 8 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 8 =
2 p --- (3)
(2) = (3)
6 u - 8 = 2 u + 8
6 u - 2 u = 8 + 8
4 u = 16
1 u = 16 ÷ 4 = 4
Number of marbles in the box
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 4) + 4
= 28 + 4
= 32
Answer(s): 32