Question

Savannah decides to download some new music. she downloaded 5 albums and 7 singles, and his total was $71. The next day she purchased more music from the same retailer and downloaded 3 more albums and 6 singles for a total of $48.

Assuming that all albums and singles are the same prices, how much did she spend on each album and each single? Write a system of equations to represent this situation. Then solve for the solution using the elimination method.

Answer 1

Answer:

Step-by-step explanation:

downloaded= 5 albums and 7 singles and total price is $71

Know,

           album + singles = 5+7=  12

           ∴ price÷ from total of albums and singles

              $71÷12=$5.92

 per album     = $5.92

 per single     =  $5.92

Next day;

                3+6=9

    total price =$48

                 ⇒ =$48÷9 = $5.3

     per album= $5.3

     per album= $5.3

"""""  I just try to Solve """"""

Answer 2

Answer:  Singles are $3/each and albums are $10 each.

Step-by-step explanation:

Let A and S represent the number of Albums and Singles, respectively.

We are told that:

5A + 7S = $71

and also that:

3A + 6S = $48

We have two equations and 2 unknowns.  Use elimination to find the price of one and then that will tell us the price of the other.  I'll choose to eliminate the A:

5A + 7S = $71

3A + 6S = $48

We can do the elimination in one of 2 ways:

1)  Solve one of the equations for A or S, and substitute it in the other:

3A + 6S = $48

3A  = $48 - 6S

A  = ($48 - 6S)/3

Now use this definition of A in the first equation:

5A + 7S = $71

5(($48 - 6S)/3) + 7S = $71

5(($48 - 6S)/3) + 7S = $71

$80 - 10S + 7S = $71

-3S = - 9

S = $3

Now we can find A:

5A + 7S = $71

5A + 7(3) = $71

5A + 21 = $71

A = $10

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2)  We could also modify one of the equations and then subtract to eliminate a variable:

5A + 7S = $71

3A + 6S = $48

Let's multiply the second equation by -(5/3):

-(5/3)*(3A + 6S = $48)

-5A - 10S = -90

Now add this to the first equation:

5A + 7S = $71

-5A - 10S = -80

  - 3S = - 9

S = $3 and therefore A = $10