SOLUTION: The boiling and freezing temperatures of water are different in the two scales. Assuming that these scales are both linear � they really are, so that�s not an issue � is there any

Question 350494: The boiling and freezing temperatures of water are different in the two scales. Assuming that these scales are both linear � they really are, so that�s not an issue � is there any point at which the temperature in Fahrenheit would equal that in Celsius? What I mean is, suppose we took a piece of metal and heated � or cooled � it to a particular value on the one scale. Is there any such value for which a thermometer measuring the other scale would have the same number? What would that number be, and how did you find it?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I originally thought no, but then I thought about it again and came up with the fact that the degrees in Celsius will be equal to the degrees in Fahrenheit when the temperature is -40 degrees.

I figured if it had to happen, it would happen when the degrees were negative.

I traced the degrees in Celsius from 0 going down by 1 degree at a time and saw that the difference between Celsius and Fahrenheit was getting smaller as I went further down into the negative territory.

At -40 degrees, they were the same.

I then went back and figured out how I could do that using a formula.

This is what I found.

f = 1.8*c + 32

This means that the degrees in Fahrenheit is equal to the degrees in Celsius * 1.8 + 32.

You might be more familiar with f = 9/5 * c + 32.

Since 9/5 = 1.8, these formulas are the same.

The reverse formula is:

c = (f-32) / 1.8

this means that the degrees in Celsius equals the degrees in Fahrenheit minus 32 and then divided by 1.8.

If they are to be equal, then f must equal c.

f = c implies:

1.8*c + 32 = (f-32) / 1.8

Multiply both sides of that equation by 1.8 to get:

1.8 * (1.8*c + 32) = f - 32

Add 32 to both sides of that equation to ge t:

1.8 * (1.8*c + 32) + 32 = f

Since we know that f = 1.8*c + 32, then we can substitute in this equation to get:

1.8 * (1.8*c + 32) + 32 = 1.8*c + 32

Subtract 32 from both sides of this equation to get:

1.8 * (1.8*c + 32) = 1.8*c

Divide both sides of this equation by 1.8 to get:

1.8*c + 32 = c

Subtract 32 from both sides of this equation and subtract c from both sides of this equation to get:

1.8*c - c = -32

Combine like terms to get:

.8*c = -32

Divide both sides of this equation by .8 to get:

c = -32 / .8

Simplify to get:

c = -40.

The formula confirms the empirical results.

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