Question

At what Celsius temperature will the numerical reading on the Fahrenheit thermometer be 51 ∘ less than that on the Celsius thermometer?
Express your answer using two significant figures.

I keep getting the wrong answer...

Answer 1

F to C: (C-32)/1.8

Problem interpretation: F = C-51

Answer 2

Therefore: C-32/1.8 = C-51?

Answer 3

C-32/1.8 is not degrees F.

Answer 4

Oh... :(

Answer 5

F = 1.8C + 32

Answer 6

I meant "F-32/1.8" my bad

Answer 7

C = (F - 32)/1.8

Answer 8

Yeah. That... ugh

Answer 9

You must put parentheses around F - 32.

Answer 10

Alright.

How would I get only C in the equation, though?

Answer 11

You do a substitution.

Start with:
F = C - 51

Answer 12

F = 1.8C + 32, so where you see F, replace F with what F is equal to, which is 1.8C + 32.

1.8C + 32 = C - 51

Answer 13

Oh... is this going to turn into an equivalence problem?

Answer 14

... yup

Answer 15

Okay, so then I would end up with 0.8C = (-51-32)?

Answer 16

correct

Answer 17

Okay...
I got this:
0.8C= -83
C = -103.75 degrees.

Answer 18

Correct.

Answer 19

And to cut down to two SF would make it ...
I'm not sure how to do that actually

Answer 20

-103 rounds to -100, but that's three SF

Answer 21

Now let's check.
Let's use our formula above to change -103.75 deg C to F

F = 1.8C + 32

F = 1.8(-103.75) + 32

F = -186.75 + 32

F = -154.75

Sure enough, the number -154.75 51 less than -103.75

Answer 22

Yeah, but I don't know how to round sig figs... it wants two, but the only rounding I get is three sig figs. e-e

Answer 23

I see. You need 2 significant figures.

Answer 24

Although I'm really glad you helped me through the other parts. Thanks for that

Answer 25

I used a calculator and it gave me:\[1.0\times10^{2}\]

Answer 26

I think you can use scientific notation.

-103.75 in scientific notation is -1.0375 * 10^2

Now write -1.0375 with 2 significant figures.

Answer 27

I thought 1.00 was the proper scientific notation?

Answer 28

Correct for the significant figure part, but remember it is negative.

Answer 29

1.00 has 3 sig figures. You must have 2, not 3, so use 1.0

Answer 30

Ah okay

Answer 31

... it said I got it wrong...

Answer 32

The last two were my tries at the answer we got.
http://prntscr.com/cfh3sx

Answer 33

OH

Answer 34

ARGH

Answer 35

It says "check your signs."
I mentioned above the answer is negative, so you need a negative sign before the 1.0

Answer 36

-1.0 * 10^2

Answer 37

Not so loud...

Answer 38

Ahem.

* (*silent screaming*)

Answer 39

I'm sorry, I'm an idiot

Answer 40

If you were an idiot, you'd have given up.
The fact that you're still at it until you understand it and get it right proves you are not.

Answer 41

At what Celsius temperature will the numerical reading on the Fahrenheit thermometer be 3-times more that on the Celsius thermometer?

Answer 42

Aw, thank you.

Answer 43

Set it up just like you did the first problem.
First, write an equation with F and C that is just a translation of the sentence.

Answer 44

the numerical reading on the Fahrenheit thermometer be 3-times more that on the Celsius thermometer

Answer 45

So another substitution?

Answer 46

Yes, but we are still working on the step before the substitution.

Answer 47

What is "3-times more that on the Celsius thermometer", using C for the Celsius reading?

Answer 48

3x more is just times 3 right?

Answer 49

3 times the Celsius reading
3 times C

Answer 50

F = 3C
and then combine that with the standard F conversion formula?

Answer 51

Ok.
Now we use the conversion formula and we substitute.

Answer 52

So...
1.8C+32 = 3C

Answer 53

I just want to explain something before we substitute.

Answer 54

Oh.
Yes?

Answer 55

There are two conversion formulas for F to C and for C to F.
The are:
C = (F - 32)/1.8 to convert from F to C
F = 1.8C + 32 to convert from C to F

How do we know which one to choose for the substitution step?

Answer 56

The F, because F=3C

Answer 57

F to C, I mean

Answer 58

GAH.

Answer 59

Oh, and I got this one right. Off by a couple digits but still correct

Answer 60

We go back to the question.
The question is asking for the Celsius temperature.
We need to solve for C,
There is a solution for F also, but we were not asked to find it.
Since we are solving only for C, we need to get rid of F and end up with only C in the equation.
That is why we look for a conversion that has F = some expression in C.
In this case, it is F = 1.8C + 32
After we substitute the conversion, we end up with an equation with just the variable C, so we can solve for C.

Answer 61

I got the answer right :)

Answer 62

At what Celsius temperature will the numerical reading on the Fahrenheit thermometer be 1/8 that on the Celsius thermometer?

Answer 63

Uh.. is this F = 1/8 C or F = 8 C?

Answer 64

One again, we now have

F = 3C

To get rid of F, we use F = 1.8C + 32

1.8C + 32 = 3C

Answer 65

F = (1/8)C

Answer 66

and now substitute the same way as before.

Answer 67

Alright, thank you :)

Answer 68

Mom's insulting me for being on here to get homework help...

Answer 69

Listen to your mom.
Bye.

Answer 70

... I'm trying to work on my homework, though.