Emily and Pamela have some stamps. If Emily gives 38 stamps to Pamela, Pamela will have 5 times the number of stamps as Emily. If Pamela gives 47 stamps to Emily, Emily will have
25 as many stamps as Pamela. How many stamps does Emily have at first?
|
Case 1 |
Case 2 |
|
Emily |
Pamela |
Emily |
Pamela |
Before |
7 u + 38 |
35 u - 38 |
12 u - 47 |
30 u + 47 |
Change |
- 38 |
+ 38 |
+ 47 |
- 47 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of stamps that Emily had at first is the same in both cases.
12 u - 47 = 7 u + 38
12 u - 7 u = 38 + 47
5 u = 85
1 u = 17
Number of stamps that Emily had at first
= 7 u + 38
= 7 x 17 + 38
= 119 + 38
= 157
Answer(s): 157