A video rental company offers a plan that includes a membership fee of $6 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $48 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. What is that total cost of either plan? How many DVDs is that?
6+2x = 48
Looks like 21 DVDs.
Naturally, the total cost would be $48, since the 2nd plan always costs that.
To find the total cost of each plan and the number of DVDs borrowed, we can set up equations based on the information given.
Let's assume the number of DVDs borrowed in a month is represented by 'x'.
For the first plan with a membership fee of $6 and $2 charged per DVD borrowed, the total cost can be calculated as:
Cost of membership + Cost per DVD * Number of DVDs
Total cost = $6 + $2 * x.
For the second plan with a fixed cost of $48 per month for unlimited DVD rentals, the total cost remains constant regardless of the number of DVDs borrowed.
Since the total cost is the same for both plans when enough DVDs are borrowed, we can set up an equation:
$6 + $2 * x = $48.
Simplifying the equation:
$2 * x = $48 - $6,
$2 * x = $42.
To solve for 'x', we divide both sides by $2:
x = $42 / $2,
x = 21.
Therefore, if a customer borrows 21 DVDs in a month, the total cost for both plans will be the same. The total cost for either plan would be:
Total cost = $6 + $2 * 21,
Total cost = $6 + $42,
Total cost = $48.
So, the total cost for either plan when 21 DVDs are borrowed would be $48, and the number of DVDs borrowed would be 21.