Question

a video store membership costs $21 and members pay only $2.50 to rent each video. the video store charges non - members $4 to rent each video. for what number of videos is the cost the same?

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of videos rented. The cost for members $C_m$ is the sum of the membership fee and the cost per video rental, so $C_m=21 + 2.5x$. The cost for non - members $C_{nm}$ is just the cost per video times the number of videos, so $C_{nm}=4x$.

Step2: Set the two cost - equations equal

We want to find when $C_m = C_{nm}$, so we set up the equation $21+2.5x = 4x$.

Step3: Solve the equation for $x$

First, subtract $2.5x$ from both sides: $21=4x - 2.5x$. Then simplify the right - hand side: $21 = 1.5x$. Divide both sides by $1.5$ to get $x=\frac{21}{1.5}=14$.

Answer:

14