2 way equation? (which is right?)

  • Thread starter RuroumiKenshin
  • Start date
In summary, there are different formulas for converting between Celsius and Fahrenheit, but only one is correct. The correct formula is C= (5/9)(F-32) or F= (9/5)C+32. Some books may have incorrect formulas, such as F= 2C+30, which should not be used. It is important to double check and use the correct formula for accurate conversions.
  • #1
RuroumiKenshin
2 way equation??! (which is right?)

I'm used to the formula(for converting celcius into farenhiet):
c=f+ 30 x 2. BUT, in some book (call it book B), its different. You just use F= 9/5 (C-32) and replace C with the given celcius temprature and multiply every thing by 9/5. Anyhow, I used both formulas, and got 2 different answers (and checked my work). Personally, I think the way book B put it doesn't make sense. If it makes sense to you, please explain.
 
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  • #2
Either you have a whole stack of books that should be thrown out or you are not reading them very closely. Both formulas are wrong!

For one thing you must surely know that 0 degrees Celcius is 32 degrees Fahrenheit so you can use that as a check:
Using your formula: c=f+ 30 x 2 (as you wrote it) f= 32 would give c= 32+ 60= 96! Of course, you really meant c= (f+32)*2 but that would be 64*2= 128 which is even worse! c= (f-32)*2 would give c=0 for f= 32 but gives c= (212-32)*2= 180*2= 360 degrees for the boiling point of water when it should be 100 degrees.

The formula you give for "book B":F= 9/5 (C-32) is almost exactly backwards: it should be C= (5/9)(F-32) (or F= (5/9)C + 32) so that when F= 32, C= 0 and when F= 212, C= (5/9)(180)= 5(20)= 100 degrees.
 
  • #3
Originally posted by HallsofIvy
[ The formula you give for "book B":F= 9/5 (C-32) is almost exactly backwards: it should be C= (5/9)(F-32) (or F= (5/9)C + 32) so that when F= 32, C= 0 and when F= 212, C= (5/9)(180)= 5(20)= 100 degrees.

These formulas are incompatible. Surely you mean F = (9/5)C +32?
 
  • #4
what i learn also F=(9/5)C + 32 F
when C = -40...F= -40 also...
and use calculator can get the same answer
 
  • #5
Let me (try to) make everything clear.
Take two test points :
0 C 32 F
100 C 212 F
X C Y F
(Tell me if my test points are wrong, i am not familiar with the fahrenhite system)
Now, try to solve the problem

Now, we know that the relation between X and Y is linear, so :
Y=aX+b
Apply this to the two test points
32=a*0+b
so ... b=32
Apply this to the second test point
212=a*100+32
(212-32)/100=a
a=1.8
So:
Y=1.8*X+32
or (the way people understand it more)
F = 1.8C + 32

And this is the right equation (isn't it ?)
 
  • #6
^Yes.
 
  • #7
I frequently use an approximation which resembles VMs first equation

C= (F-32)/1.8 ~ (F-30)/2

or
F= (1.8C)+32 ~ (2C)+30

The last of those relationships is much easier to do in your head and for normal temps is pretty close.

edit: opps! I fixed a sign error in the last line
 
Last edited:
  • #8
Here's what book A says:
"We frequently want to convert from one scale to another, so we need a convenient formula to help us with the conversion. The formula C= 5/9 (F-32) shows us the relationship between Celsius and Fahrenheit and allows us to change form one scale or another.
Example one:
Change 77 degrees Fahrenheit to Celsius.

Analysis:
Let F= the Fahrenheit temprature
Let C= the Celsius temprature

We'll use our formula and then simply substitute 77 for F.

Work:
C=5/9(F-32) F=77:
C=5/9(77-32)
C=5/9(45)
C=25
answer: 25 degrees Celsius"

"Example 2:
Find the Fahrenheit equivalent of 55 degrees Celsius.

Analysis:"
F= Fahrenheit
C= Celsius
"Use the same formula and then just substitue 55 for Celsius.

Work:
C= 5/9(F-32) C=55:
55=5/9(F-32)

Multiply by 9/5: 9/5(55=5/9(F-32)
99=F-32
Add 32: 131=F"



And Book B:

"F= 9/5C+ 32" (the book basically tells you to solve for C)."

"You can estimate temprature in degrees Fahrenheit by the formula
F=2 x C+30"
 
  • #9
And neither of those is what you gave in your original post!

(And, yes, I mistyped "9/5" for "5/9" myself earlier.")
 
  • #10
*Slaps head* Ahh! Stupidity Strikes Again! tsk, tsk, tsk...
Forgive my folly.
 

1. What is a 2-way equation?

A 2-way equation is a mathematical expression that shows the relationship between two variables. It typically consists of two parts, an independent variable and a dependent variable, and an equal sign in between.

2. How do I solve a 2-way equation?

To solve a 2-way equation, you must isolate the variable you are solving for on one side of the equation, and then perform the inverse operation on both sides to find the value of the variable.

3. Can a 2-way equation have more than two variables?

Yes, a 2-way equation can have more than two variables. However, it can only be solved if there are as many equations as there are variables.

4. What are the two types of 2-way equations?

The two types of 2-way equations are linear equations and quadratic equations. Linear equations have a maximum of two variables and can be graphed as a straight line, while quadratic equations have a maximum of two variables and can be graphed as a parabola.

5. How do I determine which 2-way equation is correct?

There is no single "correct" 2-way equation. Different equations can represent the same relationship between variables. It is important to choose an equation that is appropriate for the given scenario and accurately represents the relationship being studied.

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