There were white, silver and purple beads in a box. Sean put another 7 white beads and 4 purple beads in the box, then the ratio of the number of silver beads to the number of purple beads became 5 : 2. Then, he doubled the number of white beads and removed 17 purple beads. The ratio of the number of white beads to silver beads became 2 : 1. He counted and found that there were a total of 102 beads left in the box. Find the number of white beads that he had in the end.
| |
White beads |
Silver beads |
Purple beads |
Total |
| Before |
5 u - 7 |
5 u |
2 u - 4 |
|
| Change 1 |
+ 7 |
|
+ 4 |
|
After 1
|
1x5 =
5 u |
5 u |
2 u |
|
Change 2
|
+ 1x5 =
5 u |
|
- 17 |
|
After 2
|
2x5 =
10 u |
1x5 =
5 u |
2 u - 17 |
102 |
The number of silver beads remains unchanged. Make the number of silver beads the same. LCM of 1 and 5 is 5.
Total number of beads in the end
= 10 u + 5 u + 2 u - 17
= 17 u - 17
17 u - 17 = 102
17 u = 102 + 17
17 u = 119
1 u = 119 ÷ 17 = 7
Number of white beads in the end
= 10 u
= 10 x 7
= 70
Answer(s): 70
