There are some purple and black marbles in a box. If 3 purple marbles are removed from the box, the total number of marbles left will be 7 times the number of purple marbles left. If 27 black marbles are removed from the box, the total number of marbles left will be 4 times the number of purple marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Purple marbles |
Black marbles |
Purple marbles |
Black marbles |
Before |
1 u + 3 |
6 u |
1 p |
3 p + 27 |
Change |
- 3 |
|
|
- 27 |
After |
1 u |
6 u |
1 p |
3 p |
Number of black marbles in the end for Case 1
= 7 u - 1 u
= 6 u
Number of purple marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of purple marbles at first is the same for Case 1 and Case 2.
The number of black marbles at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
6 u = 3 p + 27
6 u - 27 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 9 =
3 p --- (3)
(2) = (3)
6 u - 27 = 3 u + 9
6 u - 3 u = 9 + 27
3 u = 36
1 u = 36 ÷ 3 = 12
Number of marbles in the box
= (1 u + 3) + 6 u
= 7 u + 3
= (7 x 12) + 3
= 84 + 3
= 87
Answer(s): 87