There are some grey and gold marbles in a box. If 9 grey marbles are removed from the box, the total number of marbles left will be 8 times the number of grey marbles left. If 21 gold marbles are removed from the box, the total number of marbles left will be 4 times the number of grey marbles. How many marbles are there in the box?
|
Case 1 |
Case 2 |
|
Grey marbles |
Gold marbles |
Grey marbles |
Gold marbles |
Before |
1 u + 9 |
7 u |
1 p |
3 p + 21 |
Change |
- 9 |
|
|
- 21 |
After |
1 u |
7 u |
1 p |
3 p |
Number of gold marbles in the end for Case 1
= 8 u - 1 u
= 7 u
Number of grey marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of grey marbles at first is the same for Case 1 and Case 2.
The number of gold marbles at first is also the same for Case 1 and Case 2.
1 u + 9 = 1 p --- (1)
7 u = 3 p + 21
7 u - 21 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 27 =
3 p --- (3)
(2) = (3)
7 u - 21 = 3 u + 27
7 u - 3 u = 27 + 21
4 u = 48
1 u = 48 ÷ 4 = 12
Number of marbles in the box
= (1 u + 9) + 7 u
= 8 u + 9
= (8 x 12) + 9
= 96 + 9
= 105
Answer(s): 105