Jade and Emily have some erasers. If Jade gives 10 erasers to Emily, Emily will have 4 times the number of erasers as Jade. If Emily gives 102 erasers to Jade, Jade will have
35 as many erasers as Emily. How many erasers does Jade have at first?
|
Case 1 |
Case 2 |
|
Jade |
Emily |
Jade |
Emily |
Before |
8 u + 10 |
32 u - 10 |
15 u - 102 |
25 u + 102 |
Change |
- 10 |
+ 10 |
+ 102 |
- 102 |
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 Jade had at first is the same in both cases.
15 u - 102 = 8 u + 10
15 u - 8 u = 10 + 102
7 u = 112
1 u = 16
Number of erasers that Jade had at first
= 8 u + 10
= 8 x 16 + 10
= 128 + 10
= 138
Answer(s): 138