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

DEFDBL A-Z
CLS
FOR f = -300 TO 3000
 IF f <> 0 THEN
  c = (f - 32) * 5 / 9
  r = c / f
  IF r = INT(r) THEN PRINT f, r, c
 END IF
NEXT f
PRINT : PRINT
FOR c = -300 TO 3000
 IF c <> 0 THEN
  f = c * 9 / 5 + 32
  r = f / c
  IF r = INT(r) THEN PRINT c, r, f
 END IF
NEXT c

provides:

Part 1:

 F             n              C
-40            1            -40
-4             5            -20
 5            -3            -15
 32            0             0

Part 2:

 C             n             F

-40            1            -40
 10            5             50
 160           2             320

Posted by Charlie on 2012-12-31 15:02:51