10
algebra

A gym charges $50 for a monthly membership and $5 per training session. Another gym charges $30 per month and $10 per session. After how many sessions in a month do both gyms cost the same?

A

3 sessions

B

5 sessions

C

4 sessions

D

6 sessions

Correct Answer: C

Choice C is the correct answer. Let ss be the number of sessions. Set up equations for total cost at each gym.

Gym 1: C1=50+5sC_1 = 50 + 5sGym 2: C2=30+10sC_2 = 30 + 10s

Set equal (cost is the same): 50+5s=30+10s50 + 5s = 30 + 10s50−30=10s−5s50 - 30 = 10s - 5s20=5s20 = 5ss=4s = 4

Solution: 4 sessions

Verification:

  • Gym 1: 50+5(4)=7050 + 5(4) = 70
  • Gym 2: 30+10(4)=7030 + 10(4) = 70 ✓

💡 Strategic Tip: "Break-even" problems ask where two expressions are equal.

Choice A is incorrect because at 3 sessions: Gym 1 = 65,Gym2=65, Gym 2 = 60 (not equal).

Choice B is incorrect because at 5 sessions: Gym 1 = 75,Gym2=75, Gym 2 = 80 (not equal).

Choice D is incorrect because at 6 sessions: Gym 1 = 80,Gym2=80, Gym 2 = 90 (not equal).

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Linear Functions Set 47