Linda and Julie have some pens. If Linda gives 35 pens to Julie, Julie will have 5 times the number of pens as Linda. If Julie gives 55 pens to Linda, Linda will have
35 as many pens as Julie. How many pens does Linda have at first?
|
Case 1 |
Case 2 |
|
Linda |
Julie |
Linda |
Julie |
Before |
4 u + 35 |
20 u - 35 |
9 u - 55 |
15 u + 55 |
Change |
- 35 |
+ 35 |
+ 55 |
- 55 |
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 Linda had at first is the same in both cases.
9 u - 55 = 4 u + 35
9 u - 4 u = 35 + 55
5 u = 90
1 u = 18
Number of pens that Linda had at first
= 4 u + 35
= 4 x 18 + 35
= 72 + 35
= 107
Answer(s): 107