Question

CC.3 Solve a system of equations by graphing: word problems W9J or For her parents' anniversary party, Kira is considering using one of two venues. A hotel in Stamford will cost $200 for a reservation, plus $50 per person. A restaurant in the same city will cost $75 per person, in addition to $150 for the reservation. In order to make the best decision, Kira 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