Hilda and Dana have some stamps. If Hilda gives 26 stamps to Dana, Dana will have 5 times the number of stamps as Hilda. If Dana gives 69 stamps to Hilda, Hilda will have
35 as many stamps as Dana. How many stamps does Hilda have at first?
|
Case 1 |
Case 2 |
|
Hilda |
Dana |
Hilda |
Dana |
Before |
4 u + 26 |
20 u - 26 |
9 u - 69 |
15 u + 69 |
Change |
- 26 |
+ 26 |
+ 69 |
- 69 |
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 Hilda had at first is the same in both cases.
9 u - 69 = 4 u + 26
9 u - 4 u = 26 + 69
5 u = 95
1 u = 19
Number of stamps that Hilda had at first
= 4 u + 26
= 4 x 19 + 26
= 76 + 26
= 102
Answer(s): 102