Question

2.) Helen is considering two different moving services. Service A charges a $15 monthly fee for unlimited streaming of movies and $2.50 per DVD rental. Service B charges a $12 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 AND y = 12.00 + 3.50x Which statement about the costs of the movie services is true?
A. When Helen rents fewer than 3 DVD's per month, service A will cost less per month than service B will cost.
B. When Helen rents more than 3 DVDs per month, service B will $12 more per month than service A will cost.
C. When Helen rents 3 DVDs per month, either service will cost her $22.50 per month. D. When Helen rents 6 DVDs per month, either service will cost her $27.00 per month.

Answer 1

C. When Helen rents 3 DVDs per month, either service will cost her $22.50 per month.

Explanation:

y = 15.00 + 2.50x

y = 12.00 + 3.50x

When x = 2

y = 15.00 + 2.50x

= 15.00 + 2.50(2)

= 15.00 + 5.00

= 20.000

y = 12.00 + 3.50x

= 12.00 + 3.50(2)

= 12.00 + 7.00

= 20.00

When x= 4

y = 15.00 + 2.50x

=15.00 + 2.50(4)

= 15.00 + 10.00

= 25.00

y = 12.00 + 3.50x

= 12.00 + 3.50(4)

= 12.00 + 14.00

=26.00

When x = 3

y = 15.00 + 2.50x

= 15.00 + 2.50(3)

= 15.00 + 7.50

= 22.50

y = 12.00 + 3.50x

= 12.00 + 3.50(3)

= 12.00 + 10.50

= 22.50

When x = 6

y = 15.00 + 2.50x

= 15.00 + 2.50(6)

= 15.00 + 15.00

= 30.00

y = 12.00 + 3.50x

= 12.00 + 3.50(6)

=12.00 + 21.00

= 33.00

The correct answer:

C. When Helen rents 3 DVDs per month, either service will cost her $22.50 per month.