Posted by **Elle** on Tuesday, January 20, 2009 at 3:33pm.

Determine the number of positive integers n that satisfy:

1/2 < n/n+1 < 99/101

I don't know how to solve this besides plugging in random numbers, which would take all day. Any other suggestions for a faster way to solve it?

Thank you!

- Another algebra -
**drwls**, Tuesday, January 20, 2009 at 4:44pm
The smallest number that satisfies

1/2 < (n/n+1) is 2/3

The largest number that satisfies

n/(n+1) < 99/101 is 49/50.

Here's proof of that:

49/50 = 0.980000

99/101 = 0.980198

50/51 = 0.98039

So all n/(n+1) numbers in the series

2/3, 3/4, 4/5 ... 49/50 satisfy the inequality.

There are therefore 48 numbers n that satisfy the condition.

## Answer This Question

## Related Questions

- Math - A toothpaste company did a survey at the mall. They found that 42.5% of ...
- Algebra 2 - A function is created to represent the amount of money in your ...
- geometry!!! please help me!!!! - Determine the least positive integer n for ...
- algebra - Let $x$, $y$, and $z$ be positive real numbers that satisfy \[2 \...
- Math (algebra) - Let x,y be complex numbers satisfying x+y=a xy=b, where a and b...
- Algebra - Joe picks 2 distinct numbers from the set of the first 14 positive ...
- math,algebra - can someone explain to me how to solve for the following: ...
- Math 115 #20 - Label each statement as true or false a. All integers are real ...
- algebra 101 - the sum of two integers is 10. three times one integer is 3 less ...
- algebra - The sum of 9 times a number and the reciprocal of the number is ...

More Related Questions