Shiyun and Yoko have some beads. If Shiyun gives 10 beads to Yoko, Yoko will have 3 times the number of beads as Shiyun. If Yoko gives 44 beads to Shiyun, Shiyun will have
23 as many beads as Yoko. How many beads does Shiyun have at first?
|
Case 1 |
Case 2 |
|
Shiyun |
Yoko |
Shiyun |
Yoko |
Before |
5 u + 10 |
15 u - 10 |
8 u - 44 |
12 u + 44 |
Change |
- 10 |
+ 10 |
+ 44 |
- 44 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 4 and 5 is 20.
Number of beads that Shiyun had at first is the same in both cases.
8 u - 44 = 5 u + 10
8 u - 5 u = 10 + 44
3 u = 54
1 u = 18
Number of beads that Shiyun had at first
= 5 u + 10
= 5 x 18 + 10
= 90 + 10
= 100
Answer(s): 100