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?
To find the total cost of either plan and the number of DVDs borrowed, we can set up equations for each plan and solve for the number of DVDs that make the total cost equal.
Let's denote the number of DVDs borrowed as "x".
For the first plan (membership fee and cost per DVD):
Total cost = membership fee + (cost per DVD * number of DVDs borrowed)
Total cost = $6 + ($2 * x)
For the second plan (flat monthly fee):
Total cost = Flat monthly fee = $48
Since we know that if the customer borrows enough DVDs, the two plans will cost the same amount, we can set up an equation:
$6 + ($2 * x) = $48
Now, we will solve for x to find the number of DVDs borrowed:
$2 * x = $48 - $6
$2 * x = $42
Divide both sides of the equation by $2 to isolate x:
x = $42 / $2
x = 21
So, if a customer borrows 21 DVDs in a month, both plans will cost the same amount.
To find the total cost, we can substitute the value of x (21) back into either plan's equation:
Total cost = $6 + ($2 * 21)
Total cost = $6 + $42
Total cost = $48
Therefore, the total cost of either plan is $48, and the number of DVDs borrowed is 21.
let d be the number of DVD's rented
2d + 6 = 48
2d = 42
d = 21
If the customer borrows less than 21 DVD's the first plan is better
If the customer borrows 21 DVD's s, the cost is the same
If the customer borrows more than 21, the flat rate of $48 is best.