Pamela and Hazel have some pens. If Pamela gives 21 pens to Hazel, Hazel will have 4 times the number of pens as Pamela. If Hazel gives 30 pens to Pamela, Pamela will have
25 as many pens as Hazel. How many pens does Pamela have at first?
|
Case 1 |
Case 2 |
|
Pamela |
Hazel |
Pamela |
Hazel |
Before |
7 u + 21 |
28 u - 21 |
10 u - 30 |
25 u + 30 |
Change |
- 21 |
+ 21 |
+ 30 |
- 30 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of pens in both cases remains unchanged. Make the total number of pens in both cases the same. LCM of 5 and 7 is 35.
Number of pens that Pamela had at first is the same in both cases.
10 u - 30 = 7 u + 21
10 u - 7 u = 21 + 30
3 u = 51
1 u = 17
Number of pens that Pamela had at first
= 7 u + 21
= 7 x 17 + 21
= 119 + 21
= 140
Answer(s): 140