There were red, gold and black beads in a box. Sean put another 5 red beads and 14 black beads in the box, then the ratio of the number of gold beads to the number of black beads became 4 : 3. Then, he doubled the number of red beads and removed 23 black beads. The ratio of the number of red beads to gold beads became 2 : 1. He counted and found that there were a total of 82 beads left in the box. Find the number of red beads that he had in the end.
| |
Red beads |
Gold beads |
Black beads |
Total |
| Before |
4 u - 5 |
4 u |
3 u - 14 |
|
| Change 1 |
+ 5 |
|
+ 14 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 23 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 23 |
82 |
The number of gold beads remains unchanged. Make the number of gold beads the same. LCM of 1 and 4 is 4.
Total number of beads in the end
= 8 u + 4 u + 3 u - 23
= 15 u - 23
15 u - 23 = 82
15 u = 82 + 23
15 u = 105
1 u = 105 ÷ 15 = 7
Number of red beads in the end
= 8 u
= 8 x 7
= 56
Answer(s): 56
