7

Set 12: Systems of Equations (Advanced)

Explanation

Answer: C

Two streaming services are being compared. Service A costs $10/month plus $2 per movie rental. Service B costs $5/month and $3 per movie. After how many movie rentals in one month do both cost the same?

A.

4 movies

B.

6 movies

C.

5 movies

✓ Correct
D.

3 movies

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Let mm be the number of movies. Service A: CA=10+2mC_A = 10 + 2 m Service B: CB=5+3mC_B = 5 + 3 m Set equal: 10+ 2 m = 5 + 3 m$$10- 5 = 3 m - 2 m$$5= m Solution: 5 movies Verification: - Service A: 10+2(5)=2010+ 2(5) = 20 - Service B: 5+3(5)=205+ 3(5) = 20 ✓ Strategic Tip: Break-even problems set two cost functions equal. Choice A is incorrect because at 4: A = 18,B=18, B = 17. Choice B is incorrect because at 6: A = 22,B=22, B = 23. Choice D is incorrect because at 3: A = 16,B=16, B = 14.

Key Steps:

•

The correct answer is 5 movies

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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