There were blue, green and pink beads in a box. Sean put another 4 blue beads and 7 pink beads in the box, then the ratio of the number of green beads to the number of pink beads became 4 : 3. Then, he doubled the number of blue beads and removed 24 pink beads. The ratio of the number of blue beads to green beads became 2 : 1. He counted and found that there were a total of 36 beads left in the box. Find the number of blue beads that he had in the end.
| |
Blue beads |
Green beads |
Pink beads |
Total |
| Before |
4 u - 4 |
4 u |
3 u - 7 |
|
| Change 1 |
+ 4 |
|
+ 7 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 24 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 24 |
36 |
The number of green beads remains unchanged. Make the number of green beads the same. LCM of 1 and 4 is 4.
Total number of beads in the end
= 8 u + 4 u + 3 u - 24
= 15 u - 24
15 u - 24 = 36
15 u = 36 + 24
15 u = 60
1 u = 60 ÷ 15 = 4
Number of blue beads in the end
= 8 u
= 8 x 4
= 32
Answer(s): 32
