Question

Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Mrs. Robertson is a dance teacher whose students are going to have a recital. She iscomparing two companies' prices for filming the recital and producing DVDs. Elena'sProductions charges $9 per DVD, plus $81 to come and film the recital. Oakdale Mediacharges $24 to film, plus $10 per DVD. To decide which company to use, Mrs. Robertsondetermines the number of DVDs that would make the two options equivalent in terms of cost.How much would each option cost? How many DVDs would that be?

Answer 1

In terms of cost, the number of DVD's that would make the two options equivalent is 57

Each option would cost $594

Step-by-step explanation:

Given the following:

Elena's production charges $9 per DVD plus $81 to come and film the recital.

Oakdale Media charges $24 to film, plus $10 per DVD.

Let x represent the number of DVD.

Elena's production total charges is:

9x + 81

Oakdale Media's total charge is:

24 + 10x

If the two options must be equivalent, then

9x + 81 = 24 + 10x

Subtract 9x from both sides

81 = 24 + 10x - 9x

81 = 24 + x

Subtract 24 from both sides

81 - 24 = x

57 = x

In terms of cost, the number of DVD's that would make the two options equivalent is 57

Since both options cost the same, we can use either of the expressions for costs. Using Elena's productions, we have:

9x + 81

= 9(57) + 81

= 513 + 81

= 594

That is, $594

Using Oakdale Media, we have:

24 + 10x

= 24 + 10(57)

=24 + 570

= 594

That is, $594

Each option would cost $594