Question

For her parents' anniversary party, Ellie is considering using one of two venues. A hotel in

Weston will cost $250 for a reservation, plus $25 per person. A restaurant in the same city
will cost $40 per person, in addition to $100 for the reservation. In order to make the best
decision, Ellie figures out how many attendees it would take to have the venues cost the
same amount. How many attendees would that be?

Write a system of equations, graph them, and type the solution.

Answer 1

The hotel is $250 plus $25 per person so the equation would be

y= 25x + 250

(Y is the total cost and x is the number of people)

the restaurant is $100 plus $40 per person so the equation would be

y = 40x + 100

What we want to know is which x value would make the y values equal to each other. So you can just replace the "y" in one equation with the other equation:

25x + 250 = 40x + 100

and then solve...

1. subtract 100 from both sides

25x + 150 = 40x

2. subtract 25x from both sides

150 = 15 x

3. divide both sides by 15

10 = x

you can check by plugging 10 into the original equations

25(10) + 250

250 + 250 = 500

and

40(10) + 100

400 + 100 = 500

they both cost $500 when you invite 10 people