Let's begin by listing out the given information:
Initiation fee = $21.25
Rent = $6.25 /DVD
The equation to show the total amount, D, Charlotte paid to rent x DVDs is given:
[tex]D=21.25+\text{6}.25x[/tex]If she paid a total of $83.75, how many DVDs did she rent is given by:
[tex]\begin{gathered} D=\text{21}.25+6.25x \\ D=83.75 \\ 83.75=21.25+6.25x \\ \text{Subtract ''21.25'' from both sides, we have:} \\ 83.75-21.25=6.25x \\ 62.5=6.25x\Rightarrow6.25x=62.5 \\ 6.25x=62.5 \\ \text{Divide both sides by ''6.25'', we have}\colon \\ x=\frac{62.5}{6.25}=10 \\ x=10 \end{gathered}[/tex]Therefore, Charlotte rented 10 DVDs
