[rachel32]

Hi, I'm attempting my AP Chemistry summer assignment and I have a question..

It goes..
"Ethylene glycol is the main component in automobile antifreeze.  To monitor the temperature of an auto cooling system, you intend to use a meter that reads from 0 to 100.  You devise a new temperature scale based on the approximate melting and boiling points of a typical antifreeze solution(-45 degrees C and 115 degrees C).  You wish these points to correspond to 0 degrees A and 100 degrees A, respectively"

a. Derive an expression for converting between degrees A and degrees C

okay, so i know that fist you have to find the difference in degree size..
so C's boiling point is 100, freezing is 0.. so 100-0 = 100
and C's boiling point is 115, freezing is -45.. so 115-(-45) = 160
so i know i'm multiplying by (100/160) or (5/8) somewhere..

and then i have to figure out the difference in zero point..
so to go from A to C, I have to add 45 degrees onto my zero point.

But how do i know if i do..
A(5/8)   +   45    [multiply by (5/8) and then add 45]
or..
(A+45)(5/8)  [add 45, and then multiply by (5/8)]

Thank you!

[FreeTheBee]

I think you're making a mistake here. I would suggest to start by writing the scale on some paper, so it is easier to see what is going on.
Then, perhaps start by solving the problem for the case where the antifreeze would span the range 0-160. Then in the second step you can deal with correcting for the 0 in the actual question.

[RandoFlyer]

I looks to me like you have the right idea but here is how I look at it.

You have a span of 160 degrees celsius, but you want to put it on a 100 point scale.

Therefore, each point in the scale translates to 1.6 degrees celsius.

If you were to use this expression:

A = C(5/8) + 45
Sub in 115 for C
A = 115(5/8) + 45
A = 116.875


This number isnt even on the A scale, so we know it cannot be correct


This was the expression I used:

A = (C+45)/1.6

Subbing in the same value for C here:

A = (115+45)/1.6
A = 100

So you can see that everything works out that way, to solve for degrees celsius you would just need to rearrange the expression to
solve for C:

C = A(1.6) - 45


Note: I chose to use 1.6, you can use 5/8 inversely if you choose.