Mrs. Todd is a dance teacher whose students are going to have a recital. She is comparing two companies' prices for filming the recital and producing DVDs. Belle's Productions charges $2 per DVD, plus $80 to come and film the recital. Oak Grove Media charges $70 to film, plus $4 per DVD. To decide which company to use, Mrs. Todd determines the number of DVDs that would make the two options equivalent in terms of cost. How many DVDs would that be? Write a system of equations, graph them, and type the solution.

Answer 1

Let's assume the number of DVDs that would make the two options equivalent in terms of cost is represented by the variable "x".

For Belle's Productions, the cost is $2 per DVD plus $80 to come and film the recital. So the total cost for Belle's Productions can be represented by the equation:
Cost = 2x + 80

For Oak Grove Media, the cost is $70 to film plus $4 per DVD. So the total cost for Oak Grove Media can be represented by the equation:
Cost = 4x + 70

To find the number of DVDs that would make the two options equivalent in terms of cost, we set the two equations equal to each other:
2x + 80 = 4x + 70

Subtracting 2x from both sides:
80 = 2x + 70

Subtracting 70 from both sides:
10 = 2x

Dividing both sides by 2:
5 = x

Therefore, the number of DVDs that would make the two options equivalent in terms of cost is 5.

To graph the equations, we can plot the cost for each company in terms of the number of DVDs and find their intersection point. However, this solution has been already calculated and the number of DVDs is given as 5.