d represents total sales over time and t represents time.
We are also given the increase/decrease in amount sold per month
Therefore, For DVDs, we have:
[tex]925-12t=d[/tex]
since the rate of sales is falling by 12 per month, hence the minus
And for Blu-ray, we have:
[tex]507+26t=d[/tex]
since the rate of sales is increasing by 26 per month, we have an addition.
Now we have a system of two equations.
Our approach is to solve both simultaneously through the substitution method.
We equate d in the first and second equation to get:
[tex]\begin{gathered} d=925-12t=507+26t \\ 925-12t=507+26t \\ \text{ Add 12t to both sides and subtract 507 from both sides to get:} \\ 925-507=26t+12t \\ 418=38t \\ \text{ Divide both sides by 38 to get:} \\ t=\frac{418}{38}=11 \end{gathered}[/tex]
Having found t, we substitute this value of t into either equation to get our d to be:
[tex]d=925-12(11)=507+26(11)=793[/tex]
Therefore, there will be 793 discs sold in 11 months.
