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. For what number of guests will the cost of Caterer A be the same as the cost of Caterer B? What is the cost for that number of guests?

Question

Mathematics

Gage Walters

19 March, 12:56

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. For what number of guests will the cost of Caterer A be the same as the cost of Caterer B? What is the cost for that number of guests?

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Answers (1)

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Jacquelyn Cooley · Answer 1

Answer: 10 guests, $250

Step-by-step explanation:

Use the equation y=mx+b

Plug in what you are given.

For caterer A the cost per guest is $15. This is the m value. The b value is the additional fee for setting up the tables, $100. Your equation should be y=15x+100.

Caterer B charges $20 per guest and a $50 fee to set up tables. The equation will be y=20x+50.

To find the number of guests that will result in an equal cost, set the equations equal to one another. Solve for x.

15x+100=20x+50

Do this by getting the x's all on one side (I subtracted 15x on both sides). Then subtract the 50 from both sides. This results in the equation 50=5x. Dividing by 5 will make x equal to 10.

To find the cost at this number of guests plug 10 into either equation y=15x+100 or y=20x+50. This results in a cost of $250.