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 2 years ago
Find the largest number n such that there is only one whole number that satisfies
\[\frac{8}{21}\] < \[\frac{n}{n+k}\] < \[\frac{5}{13}\]
 2 years ago
Find the largest number n such that there is only one whole number that satisfies \[\frac{8}{21}\] < \[\frac{n}{n+k}\] < \[\frac{5}{13}\]

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pythagoras123
 2 years ago
Best ResponseYou've already chosen the best response.0By 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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0i think that might depend on what the value of k is.

pythagoras123
 2 years ago
Best ResponseYou've already chosen the best response.0There 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.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=8%2F21+%3C+5%2F13 looks like very small difference.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0let'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 = 546209

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0find as large as you like, by adding zeros http://www.wolframalpha.com/input/?i=simplify+8%2F21+%2B+%285%2F13++8%2F21%291000000%2F1000001
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