Subject Area: Mathematics (Algebra)
Topic: Linear Equations
Scenario: The Community Garden Project
Your local community is planning to build a new community garden. The project manager needs your help to figure out the best way to manage resources and expenses. They have two main options for purchasing topsoil:
- Option A: Local Supplier: A local supplier sells topsoil for UGX 5,000 per bag, plus a flat delivery fee of UGX 20,000 regardless of the number of bags.
- Option B: Regional Wholesaler: A regional wholesaler sells topsoil for UGX 6,000 per bag, but offers free delivery if you purchase more than 10 bags. For 10 bags or fewer, there's a UGX 10,000 delivery fee.
The community garden needs to purchase a significant amount of topsoil, but they are unsure which option will be more cost-effective depending on the quantity.
Task:
- Formulate Equations: Write a linear equation for each option (Option A and Option B) that represents the total cost (C) based on the number of bags of topsoil (x). Be mindful of the delivery fees for each option.
- Analyze Costs:
- Calculate the total cost for 5 bags of topsoil using both options.
- Calculate the total cost for 15 bags of topsoil using both options.
- Determine the number of bags of topsoil at which both options would cost the same.
- Make a Recommendation: Based on your calculations, write a brief recommendation to the community garden project manager. Advise them on which option to choose for different quantities of topsoil, justifying your answer with your findings.