pythagoras123
  • pythagoras123
Find the largest number n such that there is only one whole number that satisfies \[\frac{8}{21}\] < \[\frac{n}{n+k}\] < \[\frac{5}{13}\]
Mathematics
chestercat
  • chestercat
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pythagoras123
  • 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
experimentX
  • experimentX
i think that might depend on what the value of k is.
pythagoras123
  • 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.

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

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