Final answer:
The equation to compute the number of people who can attend the party is $420 = $150 + $18 × (Number of people). By solving this equation, we find out that 15 people can attend the party with a budget of $420.
Step-by-step explanation:
To determine how many people can attend the party while staying within the family's $420 budget, we first need to set up an equation considering both the fixed cost and the variable cost per person. The fixed cost is for renting the space, which is $150, and the variable cost is the amount per person for food, which is $18. We can write the equation as:
Total cost = Fixed cost + (Cost per person × Number of people)
After substituting the given values into the equation:
$420 = $150 + $18 × (Number of people)
To solve for the number of people, we subtract the fixed cost from the total cost:
$420 - $150 = $270
Next, we divide the remaining amount by the cost per person to find the number of people who can attend:
$270 / $18 = 15 people
Therefore, 15 people can attend the party if the family spends $420. The correct answer is option A).