There are some silver and pink marbles in a box. If 2 silver marbles are removed from the box, the total number of marbles left will be 7 times the number of silver marbles left. If 24 pink marbles are removed from the box, the total number of marbles left will be 3 times the number of silver marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Silver marbles |
Pink marbles |
Silver marbles |
Pink marbles |
Before |
1 u + 2 |
6 u |
1 p |
2 p + 24 |
Change |
- 2 |
|
|
- 24 |
After |
1 u |
6 u |
1 p |
2 p |
Number of pink marbles in the end for Case 1
= 7 u - 1 u
= 6 u
Number of silver marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of silver marbles at first is the same for Case 1 and Case 2.
The number of pink marbles at first is also the same for Case 1 and Case 2.
1 u + 2 = 1 p --- (1)
6 u = 2 p + 24
6 u - 24 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 4 =
2 p --- (3)
(2) = (3)
6 u - 24 = 2 u + 4
6 u - 2 u = 4 + 24
4 u = 28
1 u = 28 ÷ 4 = 7
Number of marbles in the box
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 7) + 2
= 49 + 2
= 51
Answer(s): 51