At which temperature do both Centigrade and Fahrenheit show the same reading?

Question

..its our science quiz!! HELP!! =]

Answer 1

why do some people put overly complex answers instead of -40? what a waste of time

Answer 2

-40

Whilst the equations are both linear, if you were to plot them both on the same graph, you would see that the results do intersect (at -40degrees).

Another, slightly more geeky, way to get the answer is to use the 2 equations

1. F=9/5C +32 ... used to convert from centigrade (Celsius) to Fahrenheit

2. C= 5/9(F- 32).... used to convert from Fahrenheit to Centigrade (Celsius)

Firstly write the write the equations so that they are equal (C=F), and then we can solve the simultaneous equations. So it looks like this:

9/5C+32 = 5/9(F-32). (this is when Fahrenheit and Celcius/ Centigrade are equal)

Then you solve for either F or C, by substituting for either F or C into the equation above (1. if you are solving for F, or 2. if you are solving for C) lets use number 1 and solve for F

It now looks like this:

9/5C+32 = 5/9((9/5C+32)-32) (I just put in (9/5C + 32), where F used to be.

To solve it we just use some simple rules of equations to try to get C on its own

Firstly divide both sides by 5/9) and it look like this:

9(9/5C+32)/5 = ((9/5C+32)-32)

Then simplify right hand side by removing the brackets like this:

9(9/5C+32)/5 = 9/5C [of course 32-32=0]

Next simplify the left hand side by opening brackets (it is done by multiplying everything inside the brackets by 9):

(81/5C+288)/5 = 9/5C

To get rid of 5 on bottom of left hand side, you muliply both sides by 5 and get:

(81/5C+288) = 45/5C

Next remove the brackets arent needed (nothing to do outside the brackets):

81/5C+288 = 45/5C

Next move Cs together and numbers to other side (by taking 288 from both sides and taking 45/5C from both sides), and it looks like this:

81/5C-45/5C =-288

Now solve the left hand side (easy as they are both over 5C), so its just 81-45:

36/5C=-288

Next multiply both sides by 5 (gets rid of the 5 on the bottom of left hand side) and you get:

36C=-1440

Now we divide both sides by 36 (makes C= to 1), and we get:

C=-1440/36

Now whack that into a calculator and Hey Presto:

C=-40

(it also work if you substitute for C)

So the temperature at which Celcius = Fahrenheit is -40 degrees

(I hope this helped)

Answer 3

It's possible, the reading is -40.

Answer 4

-40 degrees

Answer 5

(F-32)/180=(C-0)/100 it is the formula for conversion between celcius and farenheit. when both are having same reading then F=C. So,

(F-32)=F*180/100

10F-320=18F

8F=--320

F=-40

So at -40 degree both scale read same.

Answer 6

They never do because they are different scales

Answer 7

At -40°.

(-40°C x 1.8) + 32 = (-72 + 32) = -40°F

(-40°F - 32) / 1.8 = (-72 / 1.8) = -40°C

Who the h**l gave this a thumbs down, whover you are you're a perfect Prat. No answer given is more correct than this.

Answer 8

-- 40 C = -- 40 F

Answer 9

They never do....

[Edit] - how stupid do I feel now, yes, it's -40

Hey, stop with the Thumbs down, I've already admitted that I'm a dumbass...

-43   -45.4

-42   -43.6

-41   -41.8

-40   -40

-39   -38.2

-38   -36.4

-37   -34.6

Answer 10

its -40 degrees

Answer 11

minus 40 is the same on both scales.

Answer 12

F=1.8C +32

substituting F = C

C = 1.8C + 32

-32 = 1.8C - C

-32 = 0.8C

  C = -32/8

  C = -40

so,

Celsius and Fahrenheit are equal at -40

Note: It can also be proved using the other equation:

C = ( F - 32 ) / 1.8

Answer 13

-40