Algebra word problem

Question

A CD costs $5.96 more at Sam's. How much would 6 CDs and 2 DVDs cost if 5 Cds and 2 DVDs cost $127.73

Answer 1

The first step is to define our variables. We ultimately want to find the "cost" of something. We need to know how much CD's cost, and how much DVD's cost. We will define are unknowns as: 

 

x = cost of a CD

y = cost of a DVD

 

 

We know that the CD costs $5.96 more than a DVD (I presume that's what the first sentence is saying, the wording is a bit sloppy in the problem statement). 

 

That means the cost of a CD (x) is equal to the cost of a DVD (y) plus $5.96:

 

x = y +$5.69

 

We have one equation and two unknowns. To get the second equation, we know 5 CD's and 2 DVD's cost $127.73 in total. Therefore: 

 

5x+2y = $127.73

 

Now we have two equations and 2 unknowns. 

 

x - y =   $5.96                                     (1)

5x+2y = $127.73                                (2)

 

We can use either substitution or elimination to solve the system of equations. I prefer elimination since it's more time efficient usually. 

 

Multiply equation (1) by 2 and add to equation (2): 

 

 

5x +2y = $127.73

2x - 2y = $11.92

_________________ 

7x +0 = $139.65

 

7x= $139.65

 

x = $19.95

 

Now we can use the cost of a CD in equation (1) to find the cost of a dvd: 

 

 

x - y = $5.96

 

y = x - $5.96

y= $13.99

 

 

EDIT: I almost forgot the easy part. Finally we want to know the cost of 6 CD's and 2 DVD's 

 

6($19.95) + 2($13.99)

 

= $147.68