Elyse and Eva have some erasers. If Elyse gives 30 erasers to Eva, Eva will have 4 times the number of erasers as Elyse. If Eva gives 19 erasers to Elyse, Elyse will have
35 as many erasers as Eva. How many erasers does Elyse have at first?
|
Case 1 |
Case 2 |
|
Elyse |
Eva |
Elyse |
Eva |
Before |
8 u + 30 |
32 u - 30 |
15 u - 19 |
25 u + 19 |
Change |
- 30 |
+ 30 |
+ 19 |
- 19 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 5 and 8 is 40.
Number of erasers that Elyse had at first is the same in both cases.
15 u - 19 = 8 u + 30
15 u - 8 u = 30 + 19
7 u = 49
1 u = 7
Number of erasers that Elyse had at first
= 8 u + 30
= 8 x 7 + 30
= 56 + 30
= 86
Answer(s): 86