Sam decides to download some new music. She downloaded 3 albums and 10 singles, and her total was $61. The next day she purchased more music from the
same retailer and downloaded 6 more albums and 8 singles for a total of $74.
Assuming that all albums and singles are the same price, 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.

An album costs $7 while a single cost $4

Step-by-step explanation:

Let the amount spent on singles be $x while the amount spent on albums be $y

First day, she downloaded 3 albums and 10 singles that cost $61

Hence;

3y + 10x = 61 ••••••••(ii)

Second day, she downloaded 6 albums and 8 singles for $74

8x + 6y = 74 ••••••••(ii)

We now want to use elimination method to solve both equations

Multiply equation i by 2 and ii by i

20x + 6y = 122

8x + 6y = 74

Subtract ii from i now

12x = 48

x = 48/12

x = 4

Recall;

3y + 10x = 61

substitute for x

3y + 10(4) = 61

3y + 40 = 61

3y = 61-40

3y = 21

y = 21/3

y = 7

An album costs $7 while a single cost $4

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

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