There are some gold and white marbles in a container. If 10 gold marbles are removed from the container, the total number of marbles left will be 7 times the number of gold marbles left. If 24 white marbles are removed from the container, the total number of marbles left will be 3 times the number of gold marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Gold marbles |
White marbles |
Gold marbles |
White marbles |
Before |
1 u + 10 |
6 u |
1 p |
2 p + 24 |
Change |
- 10 |
|
|
- 24 |
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 gold marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of gold 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 + 10 = 1 p --- (1)
6 u = 2 p + 24
6 u - 24 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 20 =
2 p --- (3)
(2) = (3)
6 u - 24 = 2 u + 20
6 u - 2 u = 20 + 24
4 u = 44
1 u = 44 ÷ 4 = 11
Number of marbles in the container
= (1 u + 10) + 6 u
= 7 u + 10
= (7 x 11) + 10
= 77 + 10
= 87
Answer(s): 87