There were red, pink and gold beads in a container. Sean put another 9 red beads and 10 gold beads in the container, then the ratio of the number of pink beads to the number of gold beads became 4 : 3. Then, he doubled the number of red beads and removed 28 gold beads. The ratio of the number of red beads to pink beads became 2 : 1. He counted and found that there were a total of 62 beads left in the container. Find the number of red beads that he had at first.
| |
Red beads |
Pink beads |
Gold beads |
Total |
| Before |
4 u - 9 |
4 u |
3 u - 10 |
|
| Change 1 |
+ 9 |
|
+ 10 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 28 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 28 |
62 |
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 - 28
= 15 u - 28
15 u - 28 = 62
15 u = 62 + 28
15 u = 90
1 u = 90 ÷ 15 = 6
Number of red beads at first
= 4 u - 9
= 4 x 6 - 9
= 24 - 9
= 15
Answer(s): 15
