a) Write the equation that represents the cost of the banquet b) determine the cost for 200 people c) how many people could attend for $2330

Question

A restaurant has banquet facilities for 300 people. When the owner quotes a price for a banquet he is including the room rent plus the cost of a meal. A banquet for 50 people costs $800 while a banquet for 100 people costs $ 1250

Answer 1

This problem describes a system of linear equations because it has two unknowns (room cost and meal cost) which will become our variables x and y.  Let x = room cost and y = meal cost.

 

A banquet for 50 people would be 50 meals at $y each plus the cost of the room at $x.  Therefore:

 

x + 50y = 800

 

A banquet for 100 people would be 100 meals at $y each plus the cost of the room at $x.  Therefore:

 

x + 100y = 1250.

 

If you solve both equations for x:

 

x = 800 - 50y and x = 1250 - 100y

 

You can now set the equations equal since they both equal the same amount, x, then solve for y.

 

800 - 50y = 1250 - 100y

800 = 1250 - 50y

-450 = -50y

9 = y

 

Each meal costs $9.  Using one of the solved for x equations, you can plug y in to find the value of x.

 

x = 800 - 50(9) = 800 - 450 = 350

 

The room costs $350.

 

Now you have all the information you need to answer to two parts:

 

A)  350 + 200(9) = 350 + 1800 = $2150

 

B) 350 + 9y = 2330

    9y = 1980

      y = 220

 

220 people could attend.