Converting Between Temperature Scales: Finding the Relationship Between M and F

[NP04]

Homework Statement

Unsatisfied with the Celsius and Fahrenheit temperature scales, you decide to create your own. On your temperature scale, the ice point is 77° M and the steam point is 437° M, where M stands for "my scale." What temperature of your scale corresponds to 68°F?

Relevant Equations

Not sure, because I think you have to make your own equations.

I found the relationship M = 2F, but got the wrong answer.

	M	F
Ice Point	77°M	32°F
Steam Point	437°M	212°F

437°M - 77°M = 360°M
212°F - 32°F = 180°F

∴ M = 2F
M = 2(68°)
M = 136°

But this is incorrect. The answer is actually 149°M. Please help.

 

[phinds]

Do a careful conversion from, say, F to C, and observe the steps. You'll see what you left out on this calculation.

 

[Vanadium 50]

I found the relationship M = 2F

Does this relationship work for 32F? For 212F?
If the answer is "no", do you think you should trust it?

 

[berkeman]

I found the relationship M = 2F, but got the wrong answer.

But this is incorrect. The answer is actually 149°M. Please help.

Hint -- make a simple 2-D linear plot of M(F) (M as a function of degrees F). You know both endpoints of the straight line between Freezing and Boiling in both M and F, so now you can find where the 68F temperature point is on the M scale. Makes sense?