Temperature is commonly measured in degrees Celsius, [tex]C[/tex], and degrees Fahrenheit, [tex]F[/tex]. To convert temperature from Fahrenheit to Celsius, we use the formula [tex]C = \frac{5}{9}(F-32)[/tex]. To find the Celsius equivalent of [tex]50^{\circ} F[/tex], you would evaluate [tex]\frac{5}{9}(50-32)[/tex].

Which expression below can also be used to convert [tex]50^{\circ} F[/tex] to degrees Celsius?

A) [tex]\frac{5}{9}(50)-5(32)[/tex]

B) [tex]5(50)-\frac{32}{9}[/tex]

We start with the well-known conversion formula from Fahrenheit to Celsius:
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]

For a temperature of [tex]$50^\circ F$[/tex], the Celsius temperature is given by
[tex]$$
C = \frac{5}{9}(50 - 32).
$$[/tex]

Evaluating the expression inside the parentheses:
[tex]$$
50 - 32 = 18,
$$[/tex]
so that
[tex]$$
C = \frac{5}{9} \times 18.
$$[/tex]

Multiplying out, we have
[tex]$$
C = \frac{5 \times 18}{9} = \frac{90}{9} = 10\,.
$$[/tex]

Now, let’s check the two alternative expressions provided:

1. Option A:
[tex]$$
\frac{5}{9}(50) - 5(32).
$$[/tex]
First, compute [tex]$\frac{5}{9}(50)$[/tex]:
[tex]$$
\frac{5 \times 50}{9} = \frac{250}{9},
$$[/tex]
and then compute [tex]$5(32)$[/tex]:
[tex]$$
5 \times 32 = 160.
$$[/tex]
Subtracting, we get:
[tex]$$
\frac{250}{9} - 160 \approx -132.22\,.
$$[/tex]

2. Option B:
[tex]$$
5(50) - \frac{32}{9}.
$$[/tex]
First, compute [tex]$5(50)$[/tex]:
[tex]$$
5 \times 50 = 250,
$$[/tex]
and then [tex]$\frac{32}{9}$[/tex]:
[tex]$$
\frac{32}{9} \approx 3.56.
$$[/tex]
Subtracting, we obtain:
[tex]$$
250 - \frac{32}{9} \approx 246.44\,.
$$[/tex]

Neither Option A nor Option B yields the correct Celsius temperature of [tex]$10^\circ C$[/tex].

Thus, neither provided expression is equivalent to [tex]$\frac{5}{9}(50-32)$[/tex], and the correct answer is that neither option works.