Gem and Wendy have some stamps. If Gem gives 11 stamps to Wendy, Wendy will have 5 times the number of stamps as Gem. If Wendy gives 122 stamps to Gem, Gem will have
23 as many stamps as Wendy. How many stamps does Gem have at first?
|
Case 1 |
Case 2 |
|
Gem |
Wendy |
Gem |
Wendy |
Before |
5 u + 11 |
25 u - 11 |
12 u - 122 |
18 u + 122 |
Change |
- 11 |
+ 11 |
+ 122 |
- 122 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 u |
The total number of stamps in both cases remains unchanged. Make the total number of stamps in both cases the same. LCM of 6 and 5 is 30.
Number of stamps that Gem had at first is the same in both cases.
12 u - 122 = 5 u + 11
12 u - 5 u = 11 + 122
7 u = 133
1 u = 19
Number of stamps that Gem had at first
= 5 u + 11
= 5 x 19 + 11
= 95 + 11
= 106
Answer(s): 106