Let's break down the problem step-by-step:
1. Initial charge for the first 2 hours:
Miguel charges [tex]$\$[/tex] 50[tex]$ for the first 2 hours of editing work. This is a fixed cost regardless of how many hours the total work takes as long as the hours exceed 2.
2. Hourly charge after the first 2 hours:
After the initial 2 hours, Miguel charges an additional $[/tex]\[tex]$ 20$[/tex] per hour. Thus, for any additional hours beyond the first 2, he charges at this rate.
3. Calculating the total charge:
Let [tex]$x$[/tex] be the total number of hours Miguel takes to complete the manuscript editing where [tex]$x > 2$[/tex].
Now, we need to determine the extra hours beyond the initial 2 hours:
[tex]\[
\text{Additional hours} = x - 2
\][/tex]
The charge for these additional hours would be:
[tex]\[
\text{Additional charge} = (x - 2) \times 20
\][/tex]
4. Total Charge Calculation:
The total cost [tex]$C$[/tex] to edit the manuscript is the sum of the fixed charge for the first 2 hours and the additional charge for the hours beyond the first 2.
[tex]\[
C = 50 + (x - 2) \times 20
\][/tex]
5. Simplifying the expression:
Let's simplify the expression for [tex]$C$[/tex]:
[tex]\[
C = 50 + 20(x - 2)
\][/tex]
[tex]\[
C = 50 + 20x - 40
\][/tex]
[tex]\[
C = 20x + 10
\][/tex]
So, the correct expression for the amount [tex]$C$[/tex] in dollars that Miguel charges if it takes him [tex]$x$[/tex] hours to edit the manuscript, where [tex]$x > 2$[/tex], is:
[tex]\[
\boxed{20x + 10}
\][/tex]
Thus, the correct answer is:
[tex]\[
\text{B) } C = 20x + 10
\][/tex]
