There were grey, purple and blue beads in a box. Sean put another 8 grey beads and 14 blue beads in the box, then the ratio of the number of purple beads to the number of blue beads became 4 : 3. Then, he doubled the number of grey beads and removed 18 blue beads. The ratio of the number of grey beads to purple beads became 2 : 1. He counted and found that there were a total of 72 beads left in the box. Find the number of grey beads that he had in the end.
| |
Grey beads |
Purple beads |
Blue beads |
Total |
| Before |
4 u - 8 |
4 u |
3 u - 14 |
|
| Change 1 |
+ 8 |
|
+ 14 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 18 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 18 |
72 |
The number of purple beads remains unchanged. Make the number of purple beads the same. LCM of 1 and 4 is 4.
Total number of beads in the end
= 8 u + 4 u + 3 u - 18
= 15 u - 18
15 u - 18 = 72
15 u = 72 + 18
15 u = 90
1 u = 90 ÷ 15 = 6
Number of grey beads in the end
= 8 u
= 8 x 6
= 48
Answer(s): 48
