Chapter 3.6, Problem 10P

To determine

To find:the fixed cost and the cost per guest.

Answer to Problem 10P

The fixed cost and the cost per guest are $100 and $8, respectively.

Explanation of Solution

Given information:

A caterer’s total cost for catering a party includes a fixed cost which is the same for every party.

The costs for serve the 25 guest is $300 and the costs for serve the 40 guest is $420.

Calculation:

Let x be a fixed cost and y be the cost per guest.

Here, x is a fixed cost for all party.

  $\text{cost}=x+y\left(\text{guest}\right)$

The costs for serve the 25 guest is $300 can be converted into equation $300=x+25y$ .

The costs for serve the 40 guest is $420can be converted into equation $420=x+40y$ .

Compute the solutions of the system $300=x+25y$ and $420=x+40y$ by linear combination method.

Subtract the equations $300=x+25y$ from $420=x+40y$ , simplify further.

  $\begin{array}{l}420=x+40y\\ 300=x+25y\\ \overline{120=0x+15x}\end{array}$

Divide on both sides by15,

  $\begin{array}{l}x=\frac{120}{15}\\ y=8\end{array}$

Substitute $y=8$ in $x+25y=300$ and simplify the value of x ,

  $\begin{array}{l}x+25\left(8\right)=300\\ x+200=300\\ x=300-200\\ x=100\end{array}$

Therefore, the fixed cost and the cost per guest are $100 and $8, respectively.