Question

A’s DJ service charges a $200 setup fee and $75 an hour after that.
B’s DJ service charges no setup fee but costs $125 an hour.
(4 points) Set up equations for both of the services using x and y. Determine the
variables and provide an explanation for why you chose what you did.
(4 points) Solve the system using the graphing method. Graph the solution on the
same coordinate plane. Interpret the coordinates of the solution in practical terms.
(4 points) Solve the system using the substitution method. (Hint: you should get
the same answer no matter which way you solve it.)
(4 points) Solve the system using the addition method. Remember to get your
equations in standard form first.
(2 points) If the party is only going to be two hours long which DJ is a better choice?
(2 points) If the party is going to be 6 hours long which DJ is a better choice?

Answer 1

The total cost includes the setup cost + per hour cost.

Let, x represents the time and y represents the total cost.

$y=200+75x$ .... (1)

Let Y represent the cost for B's DJ service.

$y=125x$ .... (2)

a. Graphing both the equations give the intersection point (solution) as (4,500)

It means for 4 hours, the total cost of both the DJ's is same at $500.

b. Substitution Method.

Plug y = 125x in equation (1)

$125x= 200+75x$

$125x-75x=200$

$50x=200$

$x=4$

$y=125\times 4 =500$

Hence, the total cost for 4 hours in both the service is $500.

c. Addition method.

Multiply equation (2) by -1

$-y = -125x$.... Equation (3).

Add euation (1) and equation (3)

$y+(-y) = 200+75x-125x$

$0=200-50x$

$50x=200, x=4$

$y=500$

Solution: For x = 4, y = 500 ( same as the previous two methods)

For x = 2, equation (1)

$y=200+(75\times 2) = 350$

For x = 2, equation (2)

$y= 125\times 2 =250$

Hence, for 2 hours, DJ B would be a better choice since it would charge $250.

For x = 6 hours, equation (1)

$y=200+(75\times 6) =650$

For x= 6, equation (2)

$y=125\times 6=750$

For 6 hours, DJ A would be  better option since it charges $650 for 6 hours.