Gwen and Julie have some stamps. If Gwen gives 26 stamps to Julie, Julie will have 3 times the number of stamps as Gwen. If Julie gives 10 stamps to Gwen, Gwen will have
23 as many stamps as Julie. How many stamps does Gwen have at first?
|
Case 1 |
Case 2 |
|
Gwen |
Julie |
Gwen |
Julie |
Before |
5 u + 26 |
15 u - 26 |
8 u - 10 |
12 u + 10 |
Change |
- 26 |
+ 26 |
+ 10 |
- 10 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of stamps in both cases remains unchanged. Make the total number of stamps in both cases the same. LCM of 4 and 5 is 20.
Number of stamps that Gwen had at first is the same in both cases.
8 u - 10 = 5 u + 26
8 u - 5 u = 26 + 10
3 u = 36
1 u = 12
Number of stamps that Gwen had at first
= 5 u + 26
= 5 x 12 + 26
= 60 + 26
= 86
Answer(s): 86