Gem and Julie have some erasers. If Gem gives 36 erasers to Julie, Julie will have 5 times the number of erasers as Gem. If Julie gives 9 erasers to Gem, Gem will have
25 as many erasers as Julie. How many erasers does Gem have at first?
|
Case 1 |
Case 2 |
|
Gem |
Julie |
Gem |
Julie |
Before |
7 u + 36 |
35 u - 36 |
12 u - 9 |
30 u + 9 |
Change |
- 36 |
+ 36 |
+ 9 |
- 9 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of erasers that Gem had at first is the same in both cases.
12 u - 9 = 7 u + 36
12 u - 7 u = 36 + 9
5 u = 45
1 u = 9
Number of erasers that Gem had at first
= 7 u + 36
= 7 x 9 + 36
= 63 + 36
= 99
Answer(s): 99