Let's determine the profit earned from selling 20 video games step-by-step using the provided functions.
1. Identify the number of units sold:
- [tex]\( x = 20 \)[/tex]
2. Revenue function calculation:
- The revenue function is [tex]\( R(x) = 60x \)[/tex].
- For [tex]\( x = 20 \)[/tex]:
[tex]\[
R(20) = 60 \times 20 = 1200
\][/tex]
3. Cost function calculation:
- The cost function is [tex]\( C(x) = 12 + 7x \)[/tex].
- For [tex]\( x = 20 \)[/tex]:
[tex]\[
C(20) = 12 + 7 \times 20 = 12 + 140 = 152
\][/tex]
4. Profit function calculation:
- The profit function is [tex]\( P(x) = R(x) - C(x) \)[/tex].
- For [tex]\( x = 20 \)[/tex]:
[tex]\[
P(20) = 1200 - 152 = 1048
\][/tex]
After completing these calculations, the profit earned from selling 20 video games is [tex]\(\$1048\)[/tex].
Thus, the correct answer is:
[tex]\(\$1048\)[/tex].
