There were pink, white and grey beads in a box. Sean put another 7 pink beads and 15 grey beads in the box, then the ratio of the number of white beads to the number of grey beads became 4 : 3. Then, he doubled the number of pink beads and removed 11 grey beads. The ratio of the number of pink beads to white beads became 2 : 1. He counted and found that there were a total of 34 beads left in the box. Find the number of pink beads that he had in the end.
| |
Pink beads |
White beads |
Grey beads |
Total |
| Before |
4 u - 7 |
4 u |
3 u - 15 |
|
| Change 1 |
+ 7 |
|
+ 15 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 11 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 11 |
34 |
The number of white beads remains unchanged. Make the number of white beads the same. LCM of 1 and 4 is 4.
Total number of beads in the end
= 8 u + 4 u + 3 u - 11
= 15 u - 11
15 u - 11 = 34
15 u = 34 + 11
15 u = 45
1 u = 45 ÷ 15 = 3
Number of pink beads in the end
= 8 u
= 8 x 3
= 24
Answer(s): 24
