A video rental company offers a plan that includes a membership fee of $8 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $14 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?

Question

A video rental company offers a plan that includes a membership fee of $8 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $14 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?

Answer 1

14+0D=8+2D

2D=6
D=3

Answer 2

To determine how many DVDs a customer needs to rent for the two plans to cost the same amount, we can set up an equation.

Let's assume the number of DVDs rented in a month is represented by 'x'.

For the first plan, the total cost can be calculated as the sum of the membership fee plus the cost per DVD multiplied by the number of DVDs rented:

Total Cost for Plan 1 = $8 + $2(x)

For the second plan, the cost is a fixed amount of $14 regardless of the number of DVDs rented.

Now we can set up the equation:

$8 + $2(x) = $14

We can simplify the equation by subtracting $8 from both sides:

$2(x) = $14 - $8

$2(x) = $6

Now we can solve for 'x' by dividing both sides of the equation by $2:

x = $6 / $2

x = 3

Therefore, a customer needs to rent 3 DVDs in a month for both plans to cost the same amount.

To calculate the total cost of either plan, we can substitute 'x' with 3 in the equation for the first plan:

Total Cost for Plan 1 = $8 + $2(3)
= $8 + $6
= $14

So, the total cost of either plan when renting 3 DVDs is $14.

Answer 3

To find out how many DVDs a customer needs to borrow in order for both plans to cost the same amount, we can set up an equation.

Let's assume the number of DVDs borrowed in a month is represented by 'x'.

For the first plan, the total cost can be calculated as follows:

Total cost of first plan = Membership fee + (Cost per DVD * Number of DVDs borrowed)
Total cost of first plan = $8 + ($2 * x)
Total cost of first plan = $8 + 2x

For the second plan, the total cost is a fixed amount of $14 per month, regardless of the number of DVDs borrowed.

Since we want to find the number of DVDs that make both plans cost the same, we can set up the equation:

$8 + 2x = $14

Now we can solve this equation to find the value of 'x'.

Subtract $8 from both sides of the equation:

2x = $14 - $8
2x = $6

Divide both sides of the equation by 2:

x = $6 / 2
x = 3

Therefore, the customer needs to borrow 3 DVDs in order for both plans to cost the same amount.

To find the total cost of either plan when borrowing 3 DVDs, we can substitute 'x' into the equation for the total cost of the first plan:

Total cost of first plan = $8 + ($2 * x)
Total cost of first plan = $8 + ($2 * 3)
Total cost of first plan = $8 + $6
Total cost of first plan = $14

So, when borrowing 3 DVDs, the total cost of either plan would be $14.