Question

Charlotte joined a DVD rental club. She paid an initiation fee of $21.25, and it costs $6.25 to rent each DVD. Write an equation to show the total amount, D, Charlotte paid to rent x DVDs. If she paid a total of $83.75, how many DVDs did she rent?

Answer 1

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:

`D=21.25+\text{6}.25x`

If she paid a total of $83.75, how many DVDs did she rent is given by:

`\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=(62.5)/(6.25)=10 \\ x=10 \end{gathered}`

Therefore, Charlotte rented 10 DVDs