7 Crystal and Martin are both joining local gyms. The gym Crystal is joining charges a one-time membership fee of \( \$ 15 \) and sessions cost \( \$ 5 \) each. The gym Martin is joining has no membership fee and sessions cost \( \$ 10 \) each. How many sessions will it take for Crystal and Martin to pay the same total amount? How much will they have paid? (B) 10 sessions; \( \$ 165 \) (B) 15 sessions; \( \$ 150 \) (C) 30 sessions; \( \$ 3 \) (D) 3 sessions; \( \$ 30 \)

Let's break it down! For Crystal, the total cost can be calculated with the formula: \( \text{Total for Crystal} = 15 + 5x \), where \( x \) is the number of sessions. For Martin, it’s simply \( \text{Total for Martin} = 10x \). To find out when they'll pay the same amount, we set the formulas equal to each other: \[ 15 + 5x = 10x \] Solving for \( x \), we get: \[ 15 = 10x - 5x \\ 15 = 5x \\ x = 3 \] So, after 3 sessions, both will have paid: \[ \text{Total} = 10(3) = 30 \text{ for Martin} \\ \text{Total} = 15 + 5(3) = 30 \text{ for Crystal} \] They both end up paying \( \$30 \) after 3 sessions. The correct answer is (D) 3 sessions; \( \$30 \). And let's sprinkle in some fun facts! Did you know gyms were pretty uncommon until the 20th century? They used to be places primarily for athletes and serious bodybuilders! Also, if you ever find yourself in a similar gym fee dilemma, consider how many sessions you realistically plan to attend. It often pays to do the math before jumping in—don’t let those 'one-time fees' lure you into spending more than you intended!