Answer:
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.