Word Problem

Question

A new website called "Sonic Music" allow you to burn music onto a CD. "Sonic Music charges an annual fee and a fee for each song downloaded. One year, Sandra downloaded 20 songs and paid $490, while Ashley downloaded 33 songs and paid $776. determine the annual fee ad the fee per song.

Answer 1

Rica, 

The first step in solving this is to define your variables.

Let f = annual fee

Let s = price per song

If Sandra downloaded 20 songs and paid $490, than the equation would be :

 

20(s) + f = $490

 

If Ashley downloaded 33 songs and paid $776, than the equation would be :

33(s) + f = $776

 

Seeing as how both equations have two variables, and they are always the same, we solve this problem as a system of equations.

 

20s + f = $490

33s + f = $776

 

Looking at these 2 equations, elimination would work for the system just as well as substitution:

Multiply the top by -1(all terms)

 

     -20s  -  f   =  -$490

+    33s  + f   =   $776

 

      13s +/-(0) =  $286

      13s           =  $286

Divide both sides by 13:

s  = $286/13

s = $22

 

Price per song is $22:

 

Substitute that value in to one of the original equations to solve for f:

 

20($22) + f = $490

$440 + f = $490

Subtract $440 from both sides:

f = $490 - $440

f = $50

 

Fee is $50 per year.

 

To check, plug both numbers into the equations, and see if you end up with true statements for both:

20($22) + $50 = $490

$440 +$50 = $490

$490 = $490   ;  true statement

 

33($22) + $50 = $776 

$726 + $50 = $776

$776 = $776   ;  true statement