a used bookstore also started selling used CDs and videos. In the first week the store sold a combination of 40 CDs and videos. They charged $4 CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold

First we must make a system of equations:
c+v=40
4c+6v=180

We can solve this system of equations using substitution
c+v=40
-v -v
_________
c=40-v

4(40-v)+6v=180
160-4x+6v=180
-160 -160
________________
2v=20
v=10

c+v=40
c+10=40
-10 -10
________
c=30

So, there are 30 CDs and 10 videos.

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PhantomWisdom PhantomWisdom · Answer 2 · 2021-12-02T12:26:48+01:00

[tex]\boldsymbol{30}[/tex] CDs and [tex]\boldsymbol{10}[/tex] videos were sold.

Let [tex]\boldsymbol{x,y}[/tex] denote number of CDs and videos respectively.

Total number of CDs and videos sold [tex]=40[/tex]

[tex]x+y=40[/tex]

[tex]\boldsymbol{y=40-x}[/tex]

Amount charged per CD [tex]=\$4[/tex]

Amount charged per video [tex]=\$6[/tex]

Also,

Total sales [tex]=\$180[/tex]

[tex]4x+6y=180[/tex]

Divide both sides by [tex]2[/tex]

[tex]\boldsymbol{2x+3y=90}[/tex]

[tex]2x+3(40-x)=90[/tex]

[tex]2x+120-3x=90[/tex]

[tex]\boldsymbol{x=30}[/tex]

So,

[tex]y=40-30[/tex]

[tex]\boldsymbol{y=10}[/tex]

Hence, [tex]30[/tex] CDs and [tex]10[/tex] videos were sold.

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