1. **Stating the problem:** Three friends want to join health clubs for different durations: D’juan for 6 months, Cho for 10 months, and Lina for 12 months. We need to determine which health club each should join to minimize their total cost. 2. **Assumptions and approach:** Since no specific prices or club options were given, we assume there are different membership plans (e.g., monthly, yearly, or school-year plans) with different pricing structures. The goal is to pick the plan that results in the lowest total cost for each friend based on their time commitment. 3. **General formula for total cost:** $$\text{Total Cost} = \text{Monthly Rate} \times \text{Number of Months}$$ If there are special plans (e.g., yearly or school-year), compare the total cost of those plans to the monthly rate multiplied by the number of months. 4. **Reasoning for each friend:** - **D’juan (6 months):** - If a monthly plan is available, paying monthly for 6 months might be cheaper than committing to a full year. - If there is a 6-month plan or a discounted half-year plan, that would be ideal. - **Cho (10 months):** - Since Cho wants to join for the school year (10 months), a school-year plan (if available) is likely the best deal. - Otherwise, paying monthly for 10 months or a yearly plan might be options, but the school-year plan usually offers savings. - **Lina (12 months):** - For a full year, a yearly membership is typically the most cost-effective. - Paying monthly for 12 months is usually more expensive than a yearly plan. 5. **Summary:** - D’juan should choose a 6-month or monthly plan. - Cho should choose a school-year plan. - Lina should choose a yearly plan. This ensures each friend pays the least amount based on their commitment length.