Math Is Fun Forum

hotgal24

Member

Registered: 2008-01-12

Posts: 4

solve this and you are a genius

What is the solution?
-*geniuises is not the answer to all question but the question to all answer*

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: solve this and you are a genius

88/19 is between 4 and 5.
Also, (88+n)/(19+n) is always less than 88/19 when n is positive.

Hence, any n that meets the requirement will make (88+n)/(19+n) somewhere between 2 and 3.
(Because then the two positive integers would be 3 and 4).

So now there are two inequalities to solve - 2<(88+n)/(19+n) and (88+n)(19+n)<3.

I

II

Depending on what the question means, all those inequalities might have to be weak (less than or equal, instead of just less than). This is important for deciding whether n=50 should be a solution.

In this case, (88+n)/(19+n) = 2. If 2 counts as between the two fractions here, then n=50 is not a solution. If it doesn't then it is.

Therefore, the values of n that work are between 16 and (49 or 50) inclusive, meaning that there are 34 or 35 solutions.

---

Why did the vector cross the road?
It wanted to be normal.