Fanny and Risa have some erasers. If Fanny gives 25 erasers to Risa, Risa will have 5 times the number of erasers as Fanny. If Risa gives 40 erasers to Fanny, Fanny will have
35 as many erasers as Risa. How many erasers does Fanny have at first?
|
Case 1 |
Case 2 |
|
Fanny |
Risa |
Fanny |
Risa |
Before |
4 u + 25 |
20 u - 25 |
9 u - 40 |
15 u + 40 |
Change |
- 25 |
+ 25 |
+ 40 |
- 40 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 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 8 is 24.
Number of erasers that Fanny had at first is the same in both cases.
9 u - 40 = 4 u + 25
9 u - 4 u = 25 + 40
5 u = 65
1 u = 13
Number of erasers that Fanny had at first
= 4 u + 25
= 4 x 13 + 25
= 52 + 25
= 77
Answer(s): 77