Question

Caterer A charges $15 per person and $100 to set up tables. Caterer B charges $20 per person and $50 to set up tables. Graph a system of equations to answer the following questions. For what number of guests will the cost of Caterer A be the same as the cost of Caterer B?

Answer 1

By setting up a system of equations for the costs of Caterer A and Caterer B, and solving for the number of guests, we find that both will charge the same amount for 10 guests.

Step-by-step explanation:

To determine for what number of guests will the cost of Caterer A be the same as Caterer B, we need to set up and solve a system of equations. Let's denote the number of guests as x and the total cost for each caterer as y.

The cost for Caterer A can be represented by the equation y = 15x + 100.

The cost for Caterer B can be represented by the equation y = 20x + 50.

Setting these two equations equal to each other, we get:

15x + 100 = 20x + 50

Solving for x, we subtract 15x from both sides:

100 = 5x + 50

Now, subtract 50 from both sides:

50 = 5x

And finally, divide both sides by 5:

x = 10

The number of guests for which both caterers will charge the same amount is 10 guests.