There were brown, grey and yellow beads in a bottle. Sean put another 5 brown beads and 6 yellow beads in the bottle, then the ratio of the number of grey beads to the number of yellow beads became 6 : 5. Then, he doubled the number of brown beads and removed 14 yellow beads. The ratio of the number of brown beads to grey beads became 2 : 1. He counted and found that there were a total of 55 beads left in the bottle. Find the number of brown beads that he had at first.
| |
Brown beads |
Grey beads |
Yellow beads |
Total |
| Before |
6 u - 5 |
6 u |
5 u - 6 |
|
| Change 1 |
+ 5 |
|
+ 6 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 14 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 14 |
55 |
The number of grey beads remains unchanged. Make the number of grey beads the same. LCM of 1 and 6 is 6.
Total number of beads in the end
= 12 u + 6 u + 5 u - 14
= 23 u - 14
23 u - 14 = 55
23 u = 55 + 14
23 u = 69
1 u = 69 ÷ 23 = 3
Number of brown beads at first
= 6 u - 5
= 6 x 3 - 5
= 18 - 5
= 13
Answer(s): 13
