Lynn and Jane have some erasers. If Lynn gives 15 erasers to Jane, Jane will have 3 times the number of erasers as Lynn. If Jane gives 36 erasers to Lynn, Lynn will have
23 as many erasers as Jane. How many erasers does Lynn have at first?
| |
Case 1 |
Case 2 |
| |
Lynn |
Jane |
Lynn |
Jane |
| Before |
5 u + 15 |
15 u - 15 |
8 u - 36 |
12 u + 36 |
| Change |
- 15 |
+ 15 |
+ 36 |
- 36 |
| After |
1x5 =
5 u |
3x5 =
15 u |
2x4 =
8 u |
3x4 =
12 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 4 and 5 is 20.
Number of erasers that Lynn had at first is the same in both cases.
8 u - 36 = 5 u + 15
8 u - 5 u = 15 + 36
3 u = 51
1 u = 17
Number of erasers that Lynn had at first
= 5 u + 15
= 5 x 17 + 15
= 85 + 15
= 100
Answer(s): 100
