Temperature Scale Conversions

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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.
MF
Ice Point77°M32°F
Steam Point437°M212°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.
 

Answers and Replies

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

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