Asset-Based Applications of Linear Equations in Remedial Math Instruction
Introduction
Mathematics plays a crucial role in understanding and solving real-world problems. In remedial math courses, it is essential to integrate culturally relevant examples to make abstract concepts, such as linear equations, more meaningful and relatable. Linear equations help analyze financial planning, business trends, and everyday decision-making processes. This module presents three exercises that highlight culturally relevant applications of linear equations to engage students effectively.
Exercise 1: Budgeting for a Food Business:
Scenario:
An entrepreneur is opening a small food truck business specializing in
jollof rice and grilled chicken. The startup costs include purchasing ingredients, renting the truck, and marketing. The entrepreneur needs to determine the number of meals to sell daily to break even.
Problem:
The business has the following cost structure:
• Fixed costs (truck rental and marketing): $1,200 per month
• Cost per meal (ingredients and preparation): $5
• Selling price per meal: $12
Using a linear equation, determine the number of meals that must be sold daily to cover the fixed costs in a 30-day month.
Solution Requirements:
- Define variables and set up a linear equation.
- Solve for the break-even point.
- Interpret the results in the context of business planning.
Exercise 2: Ride-Sharing Costs and Savings
Scenerio
A South Texas College student is trying to decide between using a ride-sharing service and purchasing a monthly bus pass. The student wants to find out when taking public transportation becomes more cost-effective.
Problem
The ride-sharing service charges a base fare of $3 plus $0.50 per mile. The monthly bus pass costs $60 for unlimited rides.
1. Write a linear equation for the total cost of using the ride-sharing service based on the number of miles traveled per month.
2. Determine the number of miles at which the bus pass becomes the cheaper option.
Solution Requirements:
- Define variables and set up equations.- Solve for the break-even mileage.- Interpret the results in the context of transportation planning.
Exercise 3: Salary and Wage Growth
Scenerio
A software developer is offered two different job contracts:
• Option A: A starting salary of $50,000 with an annual raise of $2,500.
• Option B: A starting salary of $45,000 with an annual raise of $4,000.
Problem
Using linear equations, determine how many years it will take for the salary in Option B to exceed the salary in Option A.
Solution Requirements
- Define variables and set up equations for both salary options.
- Solve for the number of years where Option B surpasses Option A.
- Interpret the results in the context of career planning.
Writing Prompt 1: Personal Financial Decisions Using Linear Equations
Think about a real-life situation where you or someone you know had to make a financial decision that could be modeled with a linear equation. This could involve budgeting, saving for a purchase, comparing two job offers, or deciding between transportation options.
1. Describe the situation and explain the financial factors involved.
2. Identify the variables and create a linear equation to model the situation.
3. Solve the equation and explain the decision based on your results.
4. Reflect on how understanding linear equations helps make informed financial choices.
5. Submit HERE.