Gwen and Linda have some pens. If Gwen gives 13 pens to Linda, Linda will have 5 times the number of pens as Gwen. If Linda gives 77 pens to Gwen, Gwen will have
35 as many pens as Linda. How many pens does Gwen have at first?
|
Case 1 |
Case 2 |
|
Gwen |
Linda |
Gwen |
Linda |
Before |
4 u + 13 |
20 u - 13 |
9 u - 77 |
15 u + 77 |
Change |
- 13 |
+ 13 |
+ 77 |
- 77 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of pens in both cases remains unchanged. Make the total number of pens in both cases the same. LCM of 6 and 8 is 24.
Number of pens that Gwen had at first is the same in both cases.
9 u - 77 = 4 u + 13
9 u - 4 u = 13 + 77
5 u = 90
1 u = 18
Number of pens that Gwen had at first
= 4 u + 13
= 4 x 18 + 13
= 72 + 13
= 85
Answer(s): 85