Gwen and Lynn have some pens. If Gwen gives 13 pens to Lynn, Lynn will have 4 times the number of pens as Gwen. If Lynn gives 11 pens to Gwen, Gwen will have
12 as many pens as Lynn. How many pens does Gwen have at first?
|
Case 1 |
Case 2 |
|
Gwen |
Lynn |
Gwen |
Lynn |
Before |
3 u + 13 |
12 u - 13 |
5 u - 11 |
10 u + 11 |
Change |
- 13 |
+ 13 |
+ 11 |
- 11 |
After |
1x3 = 3 u |
4x3 = 12 u |
1x5 = 5 u |
2x5 = 10 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 3 is 15.
Number of pens that Gwen had at first is the same in both cases.
5 u - 11 = 3 u + 13
5 u - 3 u = 13 + 11
2 u = 24
1 u = 12
Number of pens that Gwen had at first
= 3 u + 13
= 3 x 12 + 13
= 36 + 13
= 49
Answer(s): 49