Jaslyn and Linda have some beads. If Jaslyn gives 31 beads to Linda, Linda will have 5 times the number of beads as Jaslyn. If Linda gives 24 beads to Jaslyn, Jaslyn will have
25 as many beads as Linda. How many beads does Jaslyn have at first?
|
Case 1 |
Case 2 |
|
Jaslyn |
Linda |
Jaslyn |
Linda |
Before |
7 u + 31 |
35 u - 31 |
12 u - 24 |
30 u + 24 |
Change |
- 31 |
+ 31 |
+ 24 |
- 24 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of beads that Jaslyn had at first is the same in both cases.
12 u - 24 = 7 u + 31
12 u - 7 u = 31 + 24
5 u = 55
1 u = 11
Number of beads that Jaslyn had at first
= 7 u + 31
= 7 x 11 + 31
= 77 + 31
= 108
Answer(s): 108