Nicole and Penelope have some pens. If Nicole gives 11 pens to Penelope, Penelope will have 4 times the number of pens as Nicole. If Penelope gives 15 pens to Nicole, Nicole will have
12 as many pens as Penelope. How many pens does Nicole have at first?
|
Case 1 |
Case 2 |
|
Nicole |
Penelope |
Nicole |
Penelope |
Before |
3 u + 11 |
12 u - 11 |
5 u - 15 |
10 u + 15 |
Change |
- 11 |
+ 11 |
+ 15 |
- 15 |
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 Nicole had at first is the same in both cases.
5 u - 15 = 3 u + 11
5 u - 3 u = 11 + 15
2 u = 26
1 u = 13
Number of pens that Nicole had at first
= 3 u + 11
= 3 x 13 + 11
= 39 + 11
= 50
Answer(s): 50