10
algebra

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

D

3 movies

Correct Answer: C

Choice C is the correct answer. Let mm be the number of movies.

Service A: CA=10+2mC_A = 10 + 2mService B: CB=5+3mC_B = 5 + 3m

Set equal: 10+2m=5+3m10 + 2m = 5 + 3m10−5=3m−2m10 - 5 = 3m - 2m5=m5 = 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.

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Linear Functions Set 50