There were white, red and black beads in a bottle. Sean put another 2 white beads and 9 black beads in the bottle, then the ratio of the number of red beads to the number of black beads became 4 : 3. Then, he doubled the number of white beads and removed 23 black beads. The ratio of the number of white beads to red beads became 2 : 1. He counted and found that there were a total of 37 beads left in the bottle. Find the number of white beads that he had at first.
| |
White beads |
Red beads |
Black beads |
Total |
| Before |
4 u - 2 |
4 u |
3 u - 9 |
|
| Change 1 |
+ 2 |
|
+ 9 |
|
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 |
37 |
The number of red beads remains unchanged. Make the number of red 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 = 37
15 u = 37 + 23
15 u = 60
1 u = 60 ÷ 15 = 4
Number of white beads at first
= 4 u - 2
= 4 x 4 - 2
= 16 - 2
= 14
Answer(s): 14
