Penelope and Sabrina have some stamps. If Penelope gives 21 stamps to Sabrina, Sabrina will have 4 times the number of stamps as Penelope. If Sabrina gives 49 stamps to Penelope, Penelope will have
35 as many stamps as Sabrina. How many stamps does Penelope have at first?
| |
Case 1 |
Case 2 |
| |
Penelope |
Sabrina |
Penelope |
Sabrina |
| Before |
8 u + 21 |
32 u - 21 |
15 u - 49 |
25 u + 49 |
| Change |
- 21 |
+ 21 |
+ 49 |
- 49 |
| After |
1x8 =
8 u |
4x8 =
32 u |
3x5 =
15 u |
5x5 =
25 u |
The total number of stamps in both cases remains unchanged. Make the total number of stamps in both cases the same. LCM of 5 and 8 is 40.
Number of stamps that Penelope had at first is the same in both cases.
15 u - 49 = 8 u + 21
15 u - 8 u = 21 + 49
7 u = 70
1 u = 10
Number of stamps that Penelope had at first
= 8 u + 21
= 8 x 10 + 21
= 80 + 21
= 101
Answer(s): 101
