Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ A video rental company offers a plan that includes a membership fee of $\$9$ and charges $\$2$ for every DVD borrowed. They also offer a second plan, that costs $\$13$ 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? $\newline$ If a customer rents _ DVDs, each option costs $\$$ _.

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations using any method: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

A video rental company offers a plan that includes a membership fee of

\$9

and charges

\$2

for every DVD borrowed. They also offer a second plan, that costs

\$13

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?

\newline

If a customer rents _____ DVDs, each option costs

\$

_____.

Define Variables: Let's define the variables. Let $x$ be the number of DVDs rented. The first plan costs $\$9$ plus $\$2$ for every DVD, so the total cost for the first plan is $9 + 2x$ dollars. The second plan has a flat rate of $\$13$ for unlimited DVDs. We want to find out when the costs are equal.
Write Equations: Write the system of equations based on the plans. The first equation represents the first plan, and the second equation represents the second plan. Since the costs are the same when the number of DVDs rented makes the two plans equal, we have: $\newline$ First plan: $9 + 2x$ $\newline$ Second plan: $13$ $\newline$ The equation is: $9 + 2x = 13$
Solve Equation: Solve the equation for $x$ to find out how many DVDs need to be rented for the costs to be equal. $9 + 2x = 13$ Subtract $9$ from both sides to isolate the term with $x$ : $2x = 13 - 9$ $2x = 4$ Divide both sides by $2$ to solve for $x$ : $x = 4 / 2$ $x = 2$
Calculate Total Cost: Now that we know $x$ , we can find the total cost for either plan when $2$ DVDs are rented. We can substitute $x$ back into either of the original equations. Let's use the first plan's equation: $\newline$ Total cost = $9 + 2(2)$ $\newline$ Total cost = $9 + 4$ $\newline$ Total cost = $13$