Shannon and Irene have some beads. If Shannon gives 18 beads to Irene, Irene will have 4 times the number of beads as Shannon. If Irene gives 8 beads to Shannon, Shannon will have
12 as many beads as Irene. How many beads does Shannon have at first?
|
Case 1 |
Case 2 |
|
Shannon |
Irene |
Shannon |
Irene |
Before |
3 u + 18 |
12 u - 18 |
5 u - 8 |
10 u + 8 |
Change |
- 18 |
+ 18 |
+ 8 |
- 8 |
After |
1x3 = 3 u |
4x3 = 12 u |
1x5 = 5 u |
2x5 = 10 u |
The total number of beads in both cases remains unchanged. Make the total number of beads in both cases the same. LCM of 5 and 3 is 15.
Number of beads that Shannon had at first is the same in both cases.
5 u - 8 = 3 u + 18
5 u - 3 u = 18 + 8
2 u = 26
1 u = 13
Number of beads that Shannon had at first
= 3 u + 18
= 3 x 13 + 18
= 39 + 18
= 57
Answer(s): 57