There are some purple and black marbles in a box. If 10 purple marbles are removed from the box, the total number of marbles left will be 9 times the number of purple marbles left. If 10 black marbles are removed from the box, the total number of marbles left will be 3 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 + 10 |
8 u |
1 p |
2 p + 10 |
Change |
- 10 |
|
|
- 10 |
After |
1 u |
8 u |
1 p |
2 p |
Number of black marbles in the end for Case 1
= 9 u - 1 u
= 8 u
Number of purple marbles in the end for Case 2
= 3 p - 1 p
= 2 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 + 10 = 1 p --- (1)
8 u = 2 p + 10
8 u - 10 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 20 =
2 p --- (3)
(2) = (3)
8 u - 10 = 2 u + 20
8 u - 2 u = 20 + 10
6 u = 30
1 u = 30 ÷ 6 = 5
Number of marbles in the box
= (1 u + 10) + 8 u
= 9 u + 10
= (9 x 5) + 10
= 45 + 10
= 55
Answer(s): 55