Lucy and Usha have some erasers. If Lucy gives 31 erasers to Usha, Usha will have 5 times the number of erasers as Lucy. If Usha gives 54 erasers to Lucy, Lucy will have
35 as many erasers as Usha. How many erasers does Lucy have at first?
|
Case 1 |
Case 2 |
|
Lucy |
Usha |
Lucy |
Usha |
Before |
4 u + 31 |
20 u - 31 |
9 u - 54 |
15 u + 54 |
Change |
- 31 |
+ 31 |
+ 54 |
- 54 |
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 Lucy had at first is the same in both cases.
9 u - 54 = 4 u + 31
9 u - 4 u = 31 + 54
5 u = 85
1 u = 17
Number of erasers that Lucy had at first
= 4 u + 31
= 4 x 17 + 31
= 68 + 31
= 99
Answer(s): 99