To determine the profit earned from selling 20 video games, we need to use the given revenue and cost functions.
1. The revenue function [tex]\( R(x) \)[/tex] is given by:
[tex]\[
R(x) = 60x
\][/tex]
This means that for each video game sold, the revenue is [tex]$60.
2. The cost function \( C(x) \) is given by:
\[
C(x) = 12 + 7x
\]
This indicates that there is a fixed cost of $[/tex]12 and an additional cost of [tex]$7 per video game sold.
3. The profit function \( P(x) \) is defined as the difference between the revenue and the cost:
\[
P(x) = R(x) - C(x)
\]
Substituting the given functions into this formula:
\[
P(x) = 60x - (12 + 7x)
\]
4. Simplify the expression inside the parentheses:
\[
P(x) = 60x - 12 - 7x
\]
5. Combine like terms:
\[
P(x) = (60x - 7x) - 12 = 53x - 12
\]
Next, we calculate the profit for \( x = 20 \) video games sold:
6. Substitute \( x = 20 \) into the profit function \( P(x) = 53x - 12 \):
\[
P(20) = 53(20) - 12
\]
7. Perform the multiplication:
\[
53 \times 20 = 1060
\]
8. Subtract 12 from 1060:
\[
1060 - 12 = 1048
\]
Therefore, the profit earned from selling 20 video games is $[/tex]1048.
