Erika and Xandra have some erasers. If Erika gives 12 erasers to Xandra, Xandra will have 5 times the number of erasers as Erika. If Xandra gives 78 erasers to Erika, Erika will have
35 as many erasers as Xandra. How many erasers does Erika have at first?
|
Case 1 |
Case 2 |
|
Erika |
Xandra |
Erika |
Xandra |
Before |
4 u + 12 |
20 u - 12 |
9 u - 78 |
15 u + 78 |
Change |
- 12 |
+ 12 |
+ 78 |
- 78 |
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 Erika had at first is the same in both cases.
9 u - 78 = 4 u + 12
9 u - 4 u = 12 + 78
5 u = 90
1 u = 18
Number of erasers that Erika had at first
= 4 u + 12
= 4 x 18 + 12
= 72 + 12
= 84
Answer(s): 84