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xoF = (nx)oC (Posted on 2012-12-31) Difficulty: 3 of 5
If x degrees Fahrenheit = nx degrees Celsius, where each of n and x is a nonzero integer, determine all values of n and x for which this is possible.

Keeping all the other conditions unaltered, how about:
x degrees Celsius = nx degrees Fahrenheit?

Note:
Fahrenheit to Celsius:
oC= 5*(oF - 32)/9

Celsius to Fahrenheit :
oF= (C*9/5) + 32

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Some Thoughts Baby, it's warm outside (spoiler) | Comment 2 of 7 |
Rearrange the conversion formula, getting 160 = 5F - 9C

Part 1)  F = x, c = nx
            160 = 5x - 9nx
            x = 160/(5 - 9n)
            
            (5 - 9n) is always negative, so there is no solution


Part 1)  F = nx, c = x
            160 = 5nx - 9x
            x = 160/(5n - 9)
            
            5n - 9 is not a multiple of 5.
            The only divisors of 160 that are not a multiple of 5 are
               1, 2, 4, 8, 16 and 32
            5n - 9 = 1 (mod 5), 
               and the only divisors that equal 1 mod 5 are 1 and 16

            5n - 9 = 1 gives n = 2, x = 160 = C, F = 320
            5n - 9 = 16 gives n = 5, x = 10 = C,  F = 50 

           Only two answers

  Posted by Steve Herman on 2012-12-31 13:00:30
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