There were gold, green and blue marbles in a container. Sean put another 3 gold marbles and 2 blue marbles in the container, then the ratio of the number of green marbles to the number of blue marbles became 6 : 5. Then, he doubled the number of gold marbles and removed 12 blue marbles. The ratio of the number of gold marbles to green marbles became 2 : 1. He counted and found that there were a total of 126 marbles left in the container. Find the number of gold marbles that he had at first.
| |
Gold marbles |
Green marbles |
Blue marbles |
Total |
| Before |
6 u - 3 |
6 u |
5 u - 2 |
|
| Change 1 |
+ 3 |
|
+ 2 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 12 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 12 |
126 |
The number of green marbles remains unchanged. Make the number of green marbles the same. LCM of 1 and 6 is 6.
Total number of marbles in the end
= 12 u + 6 u + 5 u - 12
= 23 u - 12
23 u - 12 = 126
23 u = 126 + 12
23 u = 138
1 u = 138 ÷ 23 = 6
Number of gold marbles at first
= 6 u - 3
= 6 x 6 - 3
= 36 - 3
= 33
Answer(s): 33
