## pythagoras123 Find the largest number n such that there is only one whole number that satisfies $\frac{8}{21}$ < $\frac{n}{n+k}$ < $\frac{5}{13}$ one year ago one year ago

1. pythagoras123

By the way, it would be helpful to show how you arrived at the answer. P.S. X < Y < Z means that value Y is greater than X but smaller than Z. e.g. 11 < 17 < 25

2. experimentX

i think that might depend on what the value of k is.

3. pythagoras123

There can be many possible values for n, that reduce k to one value (meaning that the number k is determined by value of n. However, the largest value of n is requested by the question. Thus there can be only one possible value of k for some values of n. Find the highest of that group of values.

4. experimentX

http://www.wolframalpha.com/input/?i=8%2F21+%3C+5%2F13 looks like very small difference.

5. experimentX

let's construct a number between them ... http://www.wolframalpha.com/input/?i=simplify+8%2F21+%2B+%285%2F13+-+8%2F21%29%2F2 n = 209 and k = 546-209

6. experimentX

find as large as you like, by adding zeros http://www.wolframalpha.com/input/?i=simplify+8%2F21+%2B+%285%2F13+-+8%2F21%291000000%2F1000001