Betty and Kylie have some pens. If Betty gives 14 pens to Kylie, Kylie will have 5 times the number of pens as Betty. If Kylie gives 76 pens to Betty, Betty will have
35 as many pens as Kylie. How many pens does Betty have at first?
|
Case 1 |
Case 2 |
|
Betty |
Kylie |
Betty |
Kylie |
Before |
4 u + 14 |
20 u - 14 |
9 u - 76 |
15 u + 76 |
Change |
- 14 |
+ 14 |
+ 76 |
- 76 |
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 Betty had at first is the same in both cases.
9 u - 76 = 4 u + 14
9 u - 4 u = 14 + 76
5 u = 90
1 u = 18
Number of pens that Betty had at first
= 4 u + 14
= 4 x 18 + 14
= 72 + 14
= 86
Answer(s): 86