Capacity Limits Answer Key
About This Worksheet
This worksheet helps seventh-grade students solve inequalities involving maximum capacity and weight limits. The situations include buses, science labs, storage bins, event rooms, equipment racks, boats, supply carts, and theater seating. Students must determine how many groups, boxes, cases, containers, or classes can fit without going over the stated limit. This gives inequalities a clear practical meaning because the answers describe the greatest possible whole-number amount. The worksheet also encourages careful interpretation when a decimal solution must be converted into a realistic whole-number answer.
What Students Practice
Students write inequalities that combine a starting amount with a repeated amount per group or item. They then solve the inequalities and determine the maximum whole-number value that satisfies the condition. Some problems involve weight, while others involve people or seating capacity, so students must pay attention to the units. After solving, they record the greatest number that can actually fit within the limit. This gives them practice with multi-step inequalities, whole-number interpretation, and real-world constraints.
Why This Matters
Capacity problems are a natural way to show why inequalities are useful. A bus, room, shelf, or cart cannot simply hold any amount; it has a limit that must not be exceeded. Students also learn that an answer like 5.8 groups does not mean 5.8 complete groups can fit. They need to think about the situation and choose the greatest whole number that still works. This helps connect algebra with practical decision making.
Teaching Tips
Ask students to identify the maximum first and then the amount used by each group or item. Encourage them to write the inequality before calculating so they can see exactly what the limit is controlling. After solving, remind them to ask whether the variable can be fractional in the real situation. If it represents groups, boxes, classes, or containers, the final answer usually needs to be a whole number. Have them check the answer by substituting it back into the original inequality.
Curriculum Standards
This worksheet supports CCSS.MATH.CONTENT.7.EE.B.4.B by having students solve real-world inequalities and interpret the solution set. It also reinforces the idea that solutions must make sense in context, especially when the variable represents a countable quantity. The activity strengthens algebraic modeling, computation, and practical reasoning. It is a good fit for classroom practice, homework, intervention, or review.