Question

Outside the US, temperature readings areusually given in degrees Celsius; within theUS, they are often given in degrees Fahrenheit.The conversion formula from Celsius, C, toFahrenheit, F, isF= 9C/5+32 A.) find the value of C if F=32. B.)find the value of C if F=50. C.) at what temp. the readings In F and in C will be the same?

Answer 1

We are asked to use the formula for converting Celsius to Fahrenheit:

`F=(9)/(5)C+32`

Therefore, if F is 32, what is C?

we use the equation given replacing F with 32 and solve for C:

`\begin{gathered} F=(9)/(5)C+32 \\ 32=(9)/(5)C+32 \\ 32-32=(9)/(5)C \\ 0=(9)/(5)C \end{gathered}`

Notice that we used 32 to replace F, and then in the process of subtracting 32 from both sides in order to isolate the unknown C, we are left with zero on the left of the equal sign, and C times the fraction 9/5 on the other.

The only way that a product can give as answer zero, is if one of the factors is zero. Then the answer is that C corresponds to 0

Part A) C is 0 degrees Celsius.

Now for part B)

What is C if F is 50?

We use the same formula, but this time replacing F with the number 50 and solving for C:

`\begin{gathered} F=(9)/(5)C+32 \\ 50=(9)/(5)C+32 \\ 50-32=(9)/(5)C \\ 18=(9)/(5)C \\ 18\cdot5=9C \\ 90=9\text{ C} \\ C\text{ = 10} \end{gathered}`

So in this case, the Celsius reading is 10 degrees

Now part C)

We want to find which value of F and C will give equal numbers, that is when C = F

So we use again the formula, and this time replace F with C, and solve the equation for C:

`\begin{gathered} F=(9)/(5)C+32 \\ C=(9)/(5)C+32 \\ -32=(9)/(5)C-C \\ -32=(4)/(5)C \\ -32\cdot5=4C \\ -160=4C \\ C=(-160)/(4) \\ C=-40 \end{gathered}`

Which means that both readout will coincide when the temperature is - 40 degrees