Jane and Gabby have some erasers. If Jane gives 34 erasers to Gabby, Gabby will have 5 times the number of erasers as Jane. If Gabby gives 29 erasers to Jane, Jane will have
23 as many erasers as Gabby. How many erasers does Jane have at first?
| |
Case 1 |
Case 2 |
| |
Jane |
Gabby |
Jane |
Gabby |
| Before |
5 u + 34 |
25 u - 34 |
12 u - 29 |
18 u + 29 |
| Change |
- 34 |
+ 34 |
+ 29 |
- 29 |
| After |
1x5 =
5 u |
5x5 =
25 u |
2x6 =
12 u |
3x6 =
18 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 6 and 5 is 30.
Number of erasers that Jane had at first is the same in both cases.
12 u - 29 = 5 u + 34
12 u - 5 u = 34 + 29
7 u = 63
1 u = 9
Number of erasers that Jane had at first
= 5 u + 34
= 5 x 9 + 34
= 45 + 34
= 79
Answer(s): 79
