Victoria and Julie have some pens. If Victoria gives 14 pens to Julie, Julie will have 5 times the number of pens as Victoria. If Julie gives 41 pens to Victoria, Victoria will have
35 as many pens as Julie. How many pens does Victoria have at first?
|
Case 1 |
Case 2 |
|
Victoria |
Julie |
Victoria |
Julie |
Before |
4 u + 14 |
20 u - 14 |
9 u - 41 |
15 u + 41 |
Change |
- 14 |
+ 14 |
+ 41 |
- 41 |
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 Victoria had at first is the same in both cases.
9 u - 41 = 4 u + 14
9 u - 4 u = 14 + 41
5 u = 55
1 u = 11
Number of pens that Victoria had at first
= 4 u + 14
= 4 x 11 + 14
= 44 + 14
= 58
Answer(s): 58