Question

Gloria is considering two different movie services. Service A charges a $15.00 monthly fee for unlimited streaming of movies and $2.50 per DVD rental. • Service B charges a $12.00 monthly fee for unlimited streaming of movies and $3.50 per DVD rental. The system of equations below describes the relationship between the number of DVDs rented per month (x) and the monthly cost (y), in dollars, for both services. y = 15.00 +2.50x y = 12.00 +3.50x Which statement about the costs of the movie services is true?

AWhen Gloria rents 3 DVDs per month, either service will cost her $22.50 per month.
BWhen Gloria rents 6 DVDs per month, either service will cost her $27.00 per month
CWhen Gloria rents fewer than 3 DVDs per month, service A will cost less per month than service B will cost.
DWhen Gloria rents more than 3 DVDs per month, service B will cost $12 more per month than service A will cost.​

Answer 1

A. When Gloria rents 3 DVDs per month, either service will cost her $22.50 per month.

Explanation:

To determine which statement about the costs of the movie services is true, let's evaluate each option using the given equations:

A. When Gloria rents 3 DVDs per month, let's substitute x = 3 into both equations:

For Service A: y = 15.00 + 2.50(3) = 15.00 + 7.50 = $22.50

For Service B: y = 12.00 + 3.50(3) = 12.00 + 10.50 = $22.50

Both services cost Gloria $22.50 per month when renting 3 DVDs, so option A is true.

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B. When Gloria rents 6 DVDs per month, let's substitute x = 6 into both equations:

For Service A: y = 15.00 + 2.50(6) = 15.00 + 15.00 = $30.00

For Service B: y = 12.00 + 3.50(6) = 12.00 + 21.00 = $33.00

The costs are not equal, so option B is false.

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C. When Gloria rents fewer than 3 DVDs per month, let's consider x = 2:

For Service A: y = 15.00 + 2.50(2) = 15.00 + 5.00 = $20.00

For Service B: y = 12.00 + 3.50(2) = 12.00 + 7.00 = $19.00

Service B costs less when Gloria rents fewer than 3 DVDs per month, so option C is false.

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D. When Gloria rents more than 3 DVDs per month, let's consider x = 4:

For Service A: y = 15.00 + 2.50(4) = 15.00 + 10.00 = $25.00

For Service B: y = 12.00 + 3.50(4) = 12.00 + 14.00 = $26.00

Service B costs $1.00 more than Service A when Gloria rents more than 3 DVDs per month, so option D is false.

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In conclusion, the only statement that is true is:

A. When Gloria rents 3 DVDs per month, either service will cost her $22.50 per month.