Julie and Diana have some pens. If Julie gives 34 pens to Diana, Diana will have 5 times the number of pens as Julie. If Diana gives 99 pens to Julie, Julie will have
23 as many pens as Diana. How many pens does Julie have at first?
| |
Case 1 |
Case 2 |
| |
Julie |
Diana |
Julie |
Diana |
| Before |
5 u + 34 |
25 u - 34 |
12 u - 99 |
18 u + 99 |
| Change |
- 34 |
+ 34 |
+ 99 |
- 99 |
| After |
1x5 =
5 u |
5x5 =
25 u |
2x6 =
12 u |
3x6 =
18 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 5 is 30.
Number of pens that Julie had at first is the same in both cases.
12 u - 99 = 5 u + 34
12 u - 5 u = 34 + 99
7 u = 133
1 u = 19
Number of pens that Julie had at first
= 5 u + 34
= 5 x 19 + 34
= 95 + 34
= 129
Answer(s): 129
