perplexus.info :: Just Math : Equal Temperatures

Equal Temperatures (Posted on 2016-10-31)

Find all pairs (A,B) of nonzero integers such that:

(80/A)^o Fahrenheit = (80/B)^o Celsius.

*** F = 9*C/5 + 32, where F and C respectively represents Fahrenheit and Celsius scales of temperatures.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Substitution leads to (2A-5)(2B+9)=-45.

By terms of the problem only (2A-5) can be negative, so solutions are (A,B)=(1,3), (2,18).

Posted by xdog on 2016-10-31 08:20:01

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