Wendy and Tiffany have some stamps. If Wendy gives 31 stamps to Tiffany, Tiffany will have 5 times the number of stamps as Wendy. If Tiffany gives 53 stamps to Wendy, Wendy will have
23 as many stamps as Tiffany. How many stamps does Wendy have at first?
|
Case 1 |
Case 2 |
|
Wendy |
Tiffany |
Wendy |
Tiffany |
Before |
5 u + 31 |
25 u - 31 |
12 u - 53 |
18 u + 53 |
Change |
- 31 |
+ 31 |
+ 53 |
- 53 |
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 Wendy had at first is the same in both cases.
12 u - 53 = 5 u + 31
12 u - 5 u = 31 + 53
7 u = 84
1 u = 12
Number of stamps that Wendy had at first
= 5 u + 31
= 5 x 12 + 31
= 60 + 31
= 91
Answer(s): 91