There are some gold and white marbles in a container. If 4 gold marbles are removed from the container, the total number of marbles left will be 8 times the number of gold marbles left. If 12 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 + 4 |
7 u |
1 p |
2 p + 12 |
Change |
- 4 |
|
|
- 12 |
After |
1 u |
7 u |
1 p |
2 p |
Number of white marbles in the end for Case 1
= 8 u - 1 u
= 7 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 + 4 = 1 p --- (1)
7 u = 2 p + 12
7 u - 12 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 8 =
2 p --- (3)
(2) = (3)
7 u - 12 = 2 u + 8
7 u - 2 u = 8 + 12
5 u = 20
1 u = 20 ÷ 5 = 4
Number of marbles in the container
= (1 u + 4) + 7 u
= 8 u + 4
= (8 x 4) + 4
= 32 + 4
= 36
Answer(s): 36