Risa and Xandra have some beads. If Risa gives 10 beads to Xandra, Xandra will have 5 times the number of beads as Risa. If Xandra gives 65 beads to Risa, Risa will have
35 as many beads as Xandra. How many beads does Risa have at first?
| |
Case 1 |
Case 2 |
| |
Risa |
Xandra |
Risa |
Xandra |
| Before |
4 u + 10 |
20 u - 10 |
9 u - 65 |
15 u + 65 |
| Change |
- 10 |
+ 10 |
+ 65 |
- 65 |
| 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 Risa had at first is the same in both cases.
9 u - 65 = 4 u + 10
9 u - 4 u = 10 + 65
5 u = 75
1 u = 15
Number of beads that Risa had at first
= 4 u + 10
= 4 x 15 + 10
= 60 + 10
= 70
Answer(s): 70
