To find the number of video games Trevor purchased (denoted as \( x \)), we can start with the total balance of the gift card and how much he spent on the video games.
Trevor starts with a balance of $150 and ends up with a balance of $45 after his purchases. The total amount he spent can be calculated as the initial balance minus the final balance:
\[
\text{Amount spent} = 150 - 45 = 105
\]
Since each video game costs $35, the total amount spent can also be expressed as \( 35x \), where \( x \) is the number of games purchased.
We can set up the equation based on the total amount spent:
\[
35x = 105
\]
To solve for \( x \), you could rewrite the equation:
\[
x = \frac{105}{35}
\]
It looks like the answer choices you provided are not correctly formatted. However, if you had to choose an appropriate equation based on the information, it might look like:
\[
150 - 35x = 45
\]
Which rearranges to show that Trevor's initial balance minus the money spent (which is \( 35 \cdot x \)) equals his remaining balance.
None of the given options directly match this format, but based on the insight above, you can see the relationships of the amounts involved. Thus none of the listed choices A, B, or C accurately reflect the correct equation.
If we were to reflect upon the choices given, the correct decision should have been clearer in your options.