Question

The number of DVDs sold at a store in a month was 925 and the number of DVDs sold decreased by 12 permonth. The number of Blu-ray discs sold in the same store in the same month was 507 and the number of Blu-raydiscs sold increased by 26 per month. Let d represent the number of discs sold and t represent the time inmonths.

Answer 1

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:

`925-12t=d`

since the rate of sales is falling by 12 per month, hence the minus

And for Blu-ray, we have:

`507+26t=d`

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:

`\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=(418)/(38)=11 \end{gathered}`

Having found t, we substitute this value of t into either equation to get our d to be:

`d=925-12(11)=507+26(11)=793`

Therefore, there will be 793 discs sold in 11 months.