Erika and Hazel have some pens. If Erika gives 40 pens to Hazel, Hazel will have 3 times the number of pens as Erika. If Hazel gives 14 pens to Erika, Erika will have
23 as many pens as Hazel. How many pens does Erika have at first?
|
Case 1 |
Case 2 |
|
Erika |
Hazel |
Erika |
Hazel |
Before |
5 u + 40 |
15 u - 40 |
8 u - 14 |
12 u + 14 |
Change |
- 40 |
+ 40 |
+ 14 |
- 14 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of pens in both cases remains unchanged. Make the total number of pens in both cases the same. LCM of 4 and 5 is 20.
Number of pens that Erika had at first is the same in both cases.
8 u - 14 = 5 u + 40
8 u - 5 u = 40 + 14
3 u = 54
1 u = 18
Number of pens that Erika had at first
= 5 u + 40
= 5 x 18 + 40
= 90 + 40
= 130
Answer(s): 130