There were gold, silver and blue marbles in a jar. Sean put another 2 gold marbles and 9 blue marbles in the jar, then the ratio of the number of silver marbles to the number of blue marbles became 6 : 5. Then, he doubled the number of gold marbles and removed 30 blue marbles. The ratio of the number of gold marbles to silver marbles became 2 : 1. He counted and found that there were a total of 39 marbles left in the jar. Find the number of gold marbles that he had at first.
| |
Gold marbles |
Silver marbles |
Blue marbles |
Total |
| Before |
6 u - 2 |
6 u |
5 u - 9 |
|
| Change 1 |
+ 2 |
|
+ 9 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 30 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 30 |
39 |
The number of silver marbles remains unchanged. Make the number of silver marbles the same. LCM of 1 and 6 is 6.
Total number of marbles in the end
= 12 u + 6 u + 5 u - 30
= 23 u - 30
23 u - 30 = 39
23 u = 39 + 30
23 u = 69
1 u = 69 ÷ 23 = 3
Number of gold marbles at first
= 6 u - 2
= 6 x 3 - 2
= 18 - 2
= 16
Answer(s): 16
