A caterer charges a fixed cost for preparing a dinner plus an additional cost for each person served. You know that the cost for 100 students will be $750 and the cost for 150 students will be $1050. Find the caterer's fixed cost and the cost per student served.

Question

A caterer charges a fixed cost for preparing a dinner plus an additional cost for each person served. You know that the cost for 100 students will be $750 and the cost for 150 students will be $1050. Find the caterer's fixed cost and the cost per student served.

Answer 1

Look at it as being given two ordered pairs

(100,750) and (150,1050)
let's find the equation in the form
y = mx + b, (b will be the fixed cost and m the cost per student)

slope = m = (1050-750)/(150-100) = 6

using (100,750) ...
750 = 6(100) = b
b = 150

then y = 6x + 150

(check: if x = 150, y = 6(150) + 150 = 1050 , YEAH

so the fixed cost is $150, cost per student is $6

Answer 2

To find the caterer's fixed cost and the cost per student served, we can set up a system of equations based on the given information.

Let's denote the fixed cost as "F" and the cost per student as "C".

From the first piece of information, we know that the cost for 100 students is $750. This can be represented by the equation:

100C + F = 750 ... (Equation 1)

Similarly, from the second piece of information, we know that the cost for 150 students is $1050. This can be represented by the equation:

150C + F = 1050 ... (Equation 2)

Now we can solve this system of equations to find the values of F and C.

We can start by subtracting Equation 1 from Equation 2 to eliminate the F term:

(150C + F) - (100C + F) = 1050 - 750

This simplifies to:

150C - 100C = 1050 - 750

50C = 300

Dividing both sides by 50:

C = 6

Now that we have the value of C, we can substitute it into either Equation 1 or Equation 2 to solve for F. Let's use Equation 1:

100C + F = 750

Replacing C with 6:

100(6) + F = 750

600 + F = 750

Subtracting 600 from both sides:

F = 150

Therefore, the caterer's fixed cost is $150 and the cost per student served is $6.

Answer 3

To find the caterer's fixed cost, we can subtract the additional cost from the total cost for both scenarios.

For 100 students:
Total cost - Additional cost = Fixed cost
$750 - (100 students * Cost per student) = Fixed cost ... (Equation 1)

For 150 students:
Total cost - Additional cost = Fixed cost
$1050 - (150 students * Cost per student) = Fixed cost ... (Equation 2)

We can now solve the system of equations using these two equations to find the values of the Fixed cost and Cost per student.