There were yellow, brown and grey beads in a box. Sean put another 7 yellow beads and 9 grey beads in the box, then the ratio of the number of brown beads to the number of grey beads became 6 : 5. Then, he doubled the number of yellow beads and removed 15 grey beads. The ratio of the number of yellow beads to brown beads became 2 : 1. He counted and found that there were a total of 54 beads left in the box. Find the number of yellow beads that he had in the end.
| |
Yellow beads |
Brown beads |
Grey beads |
Total |
| Before |
6 u - 7 |
6 u |
5 u - 9 |
|
| Change 1 |
+ 7 |
|
+ 9 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 15 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 15 |
54 |
The number of brown beads remains unchanged. Make the number of brown beads the same. LCM of 1 and 6 is 6.
Total number of beads in the end
= 12 u + 6 u + 5 u - 15
= 23 u - 15
23 u - 15 = 54
23 u = 54 + 15
23 u = 69
1 u = 69 ÷ 23 = 3
Number of yellow beads in the end
= 12 u
= 12 x 3
= 36
Answer(s): 36
