Gem and Yoko have some erasers. If Gem gives 22 erasers to Yoko, Yoko will have 5 times the number of erasers as Gem. If Yoko gives 41 erasers to Gem, Gem will have
23 as many erasers as Yoko. How many erasers does Gem have at first?
|
Case 1 |
Case 2 |
|
Gem |
Yoko |
Gem |
Yoko |
Before |
5 u + 22 |
25 u - 22 |
12 u - 41 |
18 u + 41 |
Change |
- 22 |
+ 22 |
+ 41 |
- 41 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of erasers that Gem had at first is the same in both cases.
12 u - 41 = 5 u + 22
12 u - 5 u = 22 + 41
7 u = 63
1 u = 9
Number of erasers that Gem had at first
= 5 u + 22
= 5 x 9 + 22
= 45 + 22
= 67
Answer(s): 67