Winnie and Anna have some pens. If Winnie gives 23 pens to Anna, Anna will have 4 times the number of pens as Winnie. If Anna gives 22 pens to Winnie, Winnie will have
25 as many pens as Anna. How many pens does Winnie have at first?
|
Case 1 |
Case 2 |
|
Winnie |
Anna |
Winnie |
Anna |
Before |
7 u + 23 |
28 u - 23 |
10 u - 22 |
25 u + 22 |
Change |
- 23 |
+ 23 |
+ 22 |
- 22 |
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 Winnie had at first is the same in both cases.
10 u - 22 = 7 u + 23
10 u - 7 u = 23 + 22
3 u = 45
1 u = 15
Number of pens that Winnie had at first
= 7 u + 23
= 7 x 15 + 23
= 105 + 23
= 128
Answer(s): 128