Kathy and Winnie have some erasers. If Kathy gives 11 erasers to Winnie, Winnie will have 5 times the number of erasers as Kathy. If Winnie gives 59 erasers to Kathy, Kathy will have
35 as many erasers as Winnie. How many erasers does Kathy have at first?
| |
Case 1 |
Case 2 |
| |
Kathy |
Winnie |
Kathy |
Winnie |
| Before |
4 u + 11 |
20 u - 11 |
9 u - 59 |
15 u + 59 |
| Change |
- 11 |
+ 11 |
+ 59 |
- 59 |
| 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 Kathy had at first is the same in both cases.
9 u - 59 = 4 u + 11
9 u - 4 u = 11 + 59
5 u = 70
1 u = 14
Number of erasers that Kathy had at first
= 4 u + 11
= 4 x 14 + 11
= 56 + 11
= 67
Answer(s): 67
