Jane and Irene have some beads. If Jane gives 15 beads to Irene, Irene will have 3 times the number of beads as Jane. If Irene gives 33 beads to Jane, Jane will have
23 as many beads as Irene. How many beads does Jane have at first?
| |
Case 1 |
Case 2 |
| |
Jane |
Irene |
Jane |
Irene |
| Before |
5 u + 15 |
15 u - 15 |
8 u - 33 |
12 u + 33 |
| Change |
- 15 |
+ 15 |
+ 33 |
- 33 |
| 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 Jane had at first is the same in both cases.
8 u - 33 = 5 u + 15
8 u - 5 u = 15 + 33
3 u = 48
1 u = 16
Number of beads that Jane had at first
= 5 u + 15
= 5 x 16 + 15
= 80 + 15
= 95
Answer(s): 95
