Fanny and Nora have some erasers. If Fanny gives 33 erasers to Nora, Nora will have 3 times the number of erasers as Fanny. If Nora gives 18 erasers to Fanny, Fanny will have
23 as many erasers as Nora. How many erasers does Fanny have at first?
| |
Case 1 |
Case 2 |
| |
Fanny |
Nora |
Fanny |
Nora |
| Before |
5 u + 33 |
15 u - 33 |
8 u - 18 |
12 u + 18 |
| Change |
- 33 |
+ 33 |
+ 18 |
- 18 |
| 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 Fanny had at first is the same in both cases.
8 u - 18 = 5 u + 33
8 u - 5 u = 33 + 18
3 u = 51
1 u = 17
Number of erasers that Fanny had at first
= 5 u + 33
= 5 x 17 + 33
= 85 + 33
= 118
Answer(s): 118
