Let C represent number of CDs and D represent number of DVDs.
We have been that The Blast Off Music Company can make a total of 500 CDs and DVDs each day. We can represent this information in an equation as:
[tex]C+D=500...(1)[/tex]
[tex]C=500-D...(1)[/tex]
We are also told that it costs $8 to make each CD, so cost of C, CDs would be [tex]8C[/tex].
It costs $10 to make each DVD, so cost of D, DVDs would be [tex]10D[/tex].
We have been given that the company can spend $4800 for production costs each day. This means that cost of C CDs and D DVDs will be equal to 4800. We can represent this information in an equation as:
[tex]8C+10D=4800...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]8(500-D)+10D=4800[/tex]
[tex]4000-8D+10D=4800[/tex]
[tex]4000+2D=4800[/tex]
[tex]4000-4000+2D=4800-4000[/tex]
[tex]2D=800[/tex]
[tex]\frac{2D}{2}=\frac{800}{2}[/tex]
[tex]D=400[/tex]
Therefore, the company can make 400 DVDs in one day.
Upon substituting [tex]D=400[/tex] in equation (1), we will get:
[tex]C=500-D \Rightarrow 500-400=100[/tex]
Therefore, the company can make 100 CDs in one day.
