perplexus.info :: Just Math : x<sup>o</sup>F = (nx)<sup>o</sup>C

x^oF = (nx)^oC (Posted on 2012-12-31)

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)

Comments: ( Back to comment list | You must be logged in to post comments.)

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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