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MMathematicsEntrepreneurshipS2 to S3Algebra

Business lab: equations for a juice business

Many young people in Rwanda start small businesses. Use algebra to decide the price, how many bottles to sell and which supplier to use.

🍹P = (p − c)x − Fequations, inequalities, simultaneous equations
LevelS2 to S3 (and IGCSE)
TimeAbout 35 min
You useLinear equations and graphs
PriceFree: no account

🎯 Aim

To use linear equations, inequalities and simultaneous equations to plan a small business.

You will learn to

  • Form and solve linear equations.
  • Solve linear inequalities.
  • Solve simultaneous equations graphically and by algebra.
  • Interpret gradient and intercept.

🧭 What to do

  1. Set the fixed costs, cost per bottle and price.
  2. Read the break-even point where the lines cross.
  3. Set a Target profit and read the inequality.
  4. Compare suppliers A and B on the second graph.
  5. Answer the questions with the class data.
  6. Write your conclusion and download your lab report.

🔬 Lab bench

📋 The data

Bottles sold per month.

🧠 Investigate: answer from the data

Type your answer and tap Check. Use 💡 Hint first; open the method only when you are stuck.

📄 My lab report

Your report collects the aim, your data table, the graphs, your answers and your conclusion. It is made on your phone or computer: nothing is sent to anyone.

Check your conclusion

Profit P = (p − c)x − F is a straight line with gradient p − c (profit per bottle) and intercept −F. Break-even is where income equals costs. A target gives an inequality such as 200x − 60 000 ≥ 50 000, so x ≥ 550. Two cost lines cross where their equations are equal: below that point one supplier is cheaper, above it the other.

➕ Get more from this experiment

📝 Free

Print the worksheet (button above), download the data, and save your report. Teachers can project this page in class.

📦 Premium Lab Pack

1 000 RWF

  • Project worksheet: plan your own class business
  • Algebra in business problems
  • Teacher guide and answer key
  • Exam-style questions with marking scheme

👩‍🏫 For teachers

Use it as a practical when apparatus is missing, as homework, or as a project. Free lesson plans help you plan, teach and assess.

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