Raeann and Shiyun have some beads. If Raeann gives 10 beads to Shiyun, Shiyun will have 5 times the number of beads as Raeann. If Shiyun gives 70 beads to Raeann, Raeann will have
35 as many beads as Shiyun. How many beads does Raeann have at first?
|
Case 1 |
Case 2 |
|
Raeann |
Shiyun |
Raeann |
Shiyun |
Before |
4 u + 10 |
20 u - 10 |
9 u - 70 |
15 u + 70 |
Change |
- 10 |
+ 10 |
+ 70 |
- 70 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 6 and 8 is 24.
Number of beads that Raeann had at first is the same in both cases.
9 u - 70 = 4 u + 10
9 u - 4 u = 10 + 70
5 u = 80
1 u = 16
Number of beads that Raeann had at first
= 4 u + 10
= 4 x 16 + 10
= 64 + 10
= 74
Answer(s): 74