Kimberly and Tammy have some pens. If Kimberly gives 16 pens to Tammy, Tammy will have 5 times the number of pens as Kimberly. If Tammy gives 75 pens to Kimberly, Kimberly will have
23 as many pens as Tammy. How many pens does Kimberly have at first?
|
Case 1 |
Case 2 |
|
Kimberly |
Tammy |
Kimberly |
Tammy |
Before |
5 u + 16 |
25 u - 16 |
12 u - 75 |
18 u + 75 |
Change |
- 16 |
+ 16 |
+ 75 |
- 75 |
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 Kimberly had at first is the same in both cases.
12 u - 75 = 5 u + 16
12 u - 5 u = 16 + 75
7 u = 91
1 u = 13
Number of pens that Kimberly had at first
= 5 u + 16
= 5 x 13 + 16
= 65 + 16
= 81
Answer(s): 81