The correct equation is C: (150 - 35)x = 45.

Here's the reasoning:

• Trevor starts with $150 on his gift card.
• He buys several video games, each costing $35.
• After buying the games, there is a balance of $45 left on the card.
• The total amount spent is the original balance ($150) minus the remaining balance ($45), which is $150 - $45 = $105.
• Since each game costs $35, the number of games purchased, $x$, can be found by dividing the total amount spent by the price per game:
  $35x = 105$ So, this simplifies to: $x = \frac{105}{35} = 3$

Thus, the equation (150 - 35)x = 45 represents the situation correctly.

Would you like further clarification or details about this problem? Here are some related questions:

1. What is the solution to $(150 - 35)x = 45$?
2. How can we rewrite the equation $35x = 105$ in terms of $x$?
3. If Trevor had spent $105, how much would be left on his gift card?
4. If the price per game were different, how would the equation change?
5. How can we represent this problem as a word problem?

Tip: Always make sure to set up an equation based on what’s given: initial amount, price per item, and remaining amount.