Budget Limits Answer Key
About This Worksheet
This worksheet helps seventh-grade students use inequalities to solve budgeting problems with spending limits. Each situation gives a total budget, a fixed cost, and a repeated cost for items such as paint sets, games, decorations, rides, experiments, downloads, or other purchases. Students write an inequality that represents the spending limit and then solve to find the greatest whole-number quantity that can be purchased. This makes the math practical because students are working with the same kind of limit they might face when planning purchases. The activity is especially useful for showing why inequality answers often need to be interpreted as whole numbers.
What Students Practice
Students identify the total amount available, subtract or account for any fixed expense, and represent the repeated cost with a variable expression. They then write an inequality showing that the total spending cannot go over the budget. After solving, students determine the greatest whole-number value that fits the situation. This gives them practice with multi-step inequalities, decimal or whole-number costs, and real-world interpretation. They also learn that a decimal algebraic answer may need to be rounded down when the variable represents a number of whole items.
Why This Matters
Budget problems are a natural example of why inequalities are useful. There is usually not one exact amount a person must spend; instead, there is a maximum amount they cannot exceed. Students also need to understand that a solution such as x ≤ 4.6 does not mean they can buy 4.6 games or 4.6 tickets. The real-world meaning tells them to choose the greatest whole number that still satisfies the inequality. This kind of reasoning builds practical money sense while strengthening algebra.
Teaching Tips
Have students identify the fixed cost and repeated cost before they write the inequality. Ask them what “stays the same” and what “changes with the number of items.” Once they solve, remind them to check whether the variable represents something that must be a whole number. If the result is not whole, ask, “Can you actually buy part of this item?” That question helps students see why they usually need to round down rather than simply round to the nearest number.
Curriculum Standards
This worksheet directly supports CCSS.MATH.CONTENT.7.EE.B.4.B by having students solve real-world problems that lead to inequalities of the form px + q ≤ r. It also reinforces interpretation of the solution set and the need to make sense of whole-number restrictions in context. The budgeting situations support mathematical modeling and practical problem solving. The worksheet is a strong fit for classwork, homework, financial-literacy connections, or multi-step inequality review.