Usha and Penelope have some stamps. If Usha gives 14 stamps to Penelope, Penelope will have 5 times the number of stamps as Usha. If Penelope gives 6 stamps to Usha, Usha will have
35 as many stamps as Penelope. How many stamps does Usha have at first?
|
Case 1 |
Case 2 |
|
Usha |
Penelope |
Usha |
Penelope |
Before |
4 u + 14 |
20 u - 14 |
9 u - 6 |
15 u + 6 |
Change |
- 14 |
+ 14 |
+ 6 |
- 6 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 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 8 is 24.
Number of stamps that Usha had at first is the same in both cases.
9 u - 6 = 4 u + 14
9 u - 4 u = 14 + 6
5 u = 20
1 u = 4
Number of stamps that Usha had at first
= 4 u + 14
= 4 x 4 + 14
= 16 + 14
= 30
Answer(s): 30