Real-World Inequalities: Which Job Gets You to $300 Fastest?
In this real-world math worksheet, students step into the shoes of someone trying to reach a financial goal of $300 by taking on one of three side gigs: dog walking, yard work, or tutoring. Each job offers a different daily rate and starting bonus, and students must figure out how many days they’d need to work to meet their goal.
To do this, students will write inequalities in the form px + q ≥ 300 — where p is the daily pay, q is the bonus, and x is the number of days worked. As they enter these expressions into the worksheet, an interactive graph is automatically generated for each inequality, giving students a powerful visual tool to interpret and compare outcomes.
Students will:
- Step into a real-life scenario involving money and goal setting
- Write and solve inequalities to model different job situations
- Generate and analyze graphs to determine which job helps reach the goal faster
- Identify intersection points between job earnings and the target goal
- Use graph-based reasoning to answer both multiple-choice and open-ended questions
Why this worksheet stands out:
- Interactive visuals: The graph updates in real time as students enter their expressions
- Multiple representations: Connects algebraic reasoning with visual interpretation
- Decision-making skills: Encourages critical thinking about real-world earnings and strategy
- Individualized learning: With randomized job data for each student, no two worksheets are alike
This activity helps students see how expressions and inequalities apply directly to real-life situations — and how graphs can be used to make smart, data-driven choices.
Learning Objective
Students will write and solve linear inequalities in the form px + q ≥ r to model real-world income scenarios. They will analyze dynamically generated graphs to determine when earnings from different jobs meet or exceed a financial goal, compare multiple income models, and interpret solution sets within context. This activity reinforces algebraic reasoning, graph interpretation, and decision-making using inequalities.
Randomization Available
This worksheet supports automatic randomization of values. Each student will receive different daily pay rates and bonuses for the three side gigs. This ensures:
- Every student writes unique inequalities
- Graphs and solution sets are personalized
- It encourages individual thinking and prevents copying
You can enable or disable randomization when assigning the worksheet.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
