Question

A video rental company offers a plan that includes a membership fee of $10 and charges $4 for every DVD borrowed. They also offer a second plan, that costs $50 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?

Write a system of equations, graph them, and type the solution.

Answer 1

Let's start by writing a system of equations:

Plan 1: C = 10 + 4D, where C is the cost of the plan and D is the number of DVDs borrowed in a month.

Plan 2: C = 50, since the cost is fixed at $50 per month for unlimited DVD rentals.

To find the number of DVDs that would make the two plans cost the same, we need to solve for D when C1 = C2.

10 + 4D = 50

Subtracting 10 from both sides:

4D = 40

Dividing both sides by 4:

D = 10

So borrowing 10 DVDs in a month would make the two plans cost the same amount.

We can graph these equations to visualize the solution. The graph of Plan 1 is a straight line with a slope of 4, intercepting the y-axis at 10. The graph of Plan 2 is a horizontal line at y = 50. The point where these two lines intersect is the solution.

the intersection point occurs at D = 10, which confirms our previous calculation.