There were brown, pink and gold beads in a box. Sean put another 10 brown beads and 2 gold beads in the box, then the ratio of the number of pink beads to the number of gold beads became 4 : 3. Then, he doubled the number of brown beads and removed 18 gold beads. The ratio of the number of brown beads to pink beads became 2 : 1. He counted and found that there were a total of 87 beads left in the box. Find the number of brown beads that he had in the end.
| |
Brown beads |
Pink beads |
Gold beads |
Total |
| Before |
4 u - 10 |
4 u |
3 u - 2 |
|
| Change 1 |
+ 10 |
|
+ 2 |
|
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 |
87 |
The number of pink beads remains unchanged. Make the number of pink 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 = 87
15 u = 87 + 18
15 u = 105
1 u = 105 ÷ 15 = 7
Number of brown beads in the end
= 8 u
= 8 x 7
= 56
Answer(s): 56
