Natalie and Tiffany have some pens. If Natalie gives 38 pens to Tiffany, Tiffany will have 5 times the number of pens as Natalie. If Tiffany gives 57 pens to Natalie, Natalie will have
25 as many pens as Tiffany. How many pens does Natalie have at first?
|
Case 1 |
Case 2 |
|
Natalie |
Tiffany |
Natalie |
Tiffany |
Before |
7 u + 38 |
35 u - 38 |
12 u - 57 |
30 u + 57 |
Change |
- 38 |
+ 38 |
+ 57 |
- 57 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 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 7 is 42.
Number of pens that Natalie had at first is the same in both cases.
12 u - 57 = 7 u + 38
12 u - 7 u = 38 + 57
5 u = 95
1 u = 19
Number of pens that Natalie had at first
= 7 u + 38
= 7 x 19 + 38
= 133 + 38
= 171
Answer(s): 171