There were green, yellow and gold marbles in a jar. Sean put another 8 green marbles and 7 gold marbles in the jar, then the ratio of the number of yellow marbles to the number of gold marbles became 6 : 5. Then, he doubled the number of green marbles and removed 26 gold marbles. The ratio of the number of green marbles to yellow marbles became 2 : 1. He counted and found that there were a total of 66 marbles left in the jar. Find the number of green marbles that he had at first.
| |
Green marbles |
Yellow marbles |
Gold marbles |
Total |
| Before |
6 u - 8 |
6 u |
5 u - 7 |
|
| Change 1 |
+ 8 |
|
+ 7 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 26 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 26 |
66 |
The number of yellow marbles remains unchanged. Make the number of yellow marbles the same. LCM of 1 and 6 is 6.
Total number of marbles in the end
= 12 u + 6 u + 5 u - 26
= 23 u - 26
23 u - 26 = 66
23 u = 66 + 26
23 u = 92
1 u = 92 ÷ 23 = 4
Number of green marbles at first
= 6 u - 8
= 6 x 4 - 8
= 24 - 8
= 16
Answer(s): 16
