Final answer:
To keep the total cost of catering under $300, Remy can invite a maximum of 29 guests. Calculating by subtracting the fixed cost from the budget limit and then dividing by the cost per guest gives us a number slightly less than 30, which we round down.
Step-by-step explanation:
The subject of this question is Mathematics. Remy wants to cater food for a party while keeping her spending under $300. The catering company charges a fixed cost of $75 plus an additional $7.50 per guest. To calculate the maximum number of guests she can invite without exceeding her budget, we need to set up an equation and solve for the number of guests.
Let's denote the number of guests as x. The total cost of the catering will be the fixed cost plus the cost per guest times the number of guests, which is $75 + $7.50x. We set this expression to be less than $300:
$75 + $7.50x < $300
Now, we solve for x:
- Subtract $75 from both sides to isolate the variable term: $7.50x < $225
- Divide both sides by $7.50 to solve for x: x < 30
Remy can invite up to 29 guests, as inviting 30 guests would bring the total cost to exactly $300, and she wants to spend under $300.