Question

- The Blast Off Music Company makes CDs and DVDs. The company can make a total of 500 CDs and DVDS

Answer 1

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:

$C+D=500...(1)$

$C=500-D...(1)$

We are also told that it costs $8 to make each CD, so cost of C, CDs would be $8C$.

It costs $10 to make each DVD, so cost of D, DVDs would be $10D$.

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:

$8C+10D=4800...(2)$

Upon substituting equation (1) in equation (2), we will get:

$8(500-D)+10D=4800$

$4000-8D+10D=4800$

$4000+2D=4800$

$4000-4000+2D=4800-4000$

$2D=800$

$\frac{2D}{2}=\frac{800}{2}$

$D=400$

Therefore, the company can make 400 DVDs in one day.

Upon substituting $D=400$ in equation (1), we will get:

$C=500-D \Rightarrow 500-400=100$

Therefore, the company can make 100 CDs in one day.