Question

a charters total cost of catering a party includes a fixed cost, which is the same for every party. in addition, the caterer chargers a certain amount for each quest. if it costs $300 to serve 25 quests and $420 to serve 40 quests, find the fixed cost and the cost per guest

Answer 1

The fixed cost for the caterer is $100, and the cost per guest is $8. These values were determined by setting up a system of equations based on the provided costs for different numbers of guests and solving for the unknowns.

Step-by-step explanation:

To determine the fixed cost and the cost per guest for catering, we can set up two equations based on the given information. Let F represent the fixed cost, and c represent the cost per guest. Our two equations based on the scenarios provided are:

• For 25 guests: F + 25c = $300
• For 40 guests: F + 40c = $420

We can solve this system of equations using substitution or elimination. Subtracting the first equation from the second gives us 15c = $120 or c = $8 as the cost per guest. By substituting c = $8 into the first equation, we can find F. So, F + 25($8) = $300 simplifies to F = $300 - $200, therefore F = $100 as the fixed cost.

The final answer is: the fixed cost is $100 and the cost per guest is $8.