A movie rental company offers two plans for its customers. The digital movie plan costs $3 per movie and no monthly fee. The DVD plan costs $10 per month plus $0.50 per movie. If a person rents movies in a month, then the two options will cost the same at $.

Make an algebraic expression for each plan.

For an instance, x represents the number of movies, and y represents the number of months

⇒ The expression for the digital movie plan is 3x

⇒ The expression for the DVD plan is 10y + 0.5x

A person rents movies in a month (that means the value of y equals 1), the expression of the DVD plan would be 10 (1) + 0.5x = 10 + 0.5x

Find the value of x when the cost of both plan are the same

The two options will cost the same when the expression for digital movie is equal to the expression for DVD

the digital movie plan = the DVD plan

3x = 10 + 0.5x

Solve for x

3x - 0.5x = 10

2.5x = 10

x = 10/2.5

x = 4

The two options will cost the same, if the person rents 4 movies