Cindy and Usha have some stamps. If Cindy gives 28 stamps to Usha, Usha will have 5 times the number of stamps as Cindy. If Usha gives 84 stamps to Cindy, Cindy will have
23 as many stamps as Usha. How many stamps does Cindy have at first?
|
Case 1 |
Case 2 |
|
Cindy |
Usha |
Cindy |
Usha |
Before |
5 u + 28 |
25 u - 28 |
12 u - 84 |
18 u + 84 |
Change |
- 28 |
+ 28 |
+ 84 |
- 84 |
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 Cindy had at first is the same in both cases.
12 u - 84 = 5 u + 28
12 u - 5 u = 28 + 84
7 u = 112
1 u = 16
Number of stamps that Cindy had at first
= 5 u + 28
= 5 x 16 + 28
= 80 + 28
= 108
Answer(s): 108