A school club has at most $240 for a banner order. The design fee is $36, and each banner costs $18. What is the greatest number of banners the club can order?
Reasoning strategy
Write 36 + 18b <= 240 and choose the greatest whole-number solution.
Difficulty Practice Guide
Hard Grade 7 Inequalities Word Problems
This page shows what hard practice should demand for grade 7 inequalities word problems. The goal is not a larger worksheet. The goal is to make the student's reasoning visible enough to choose the next better problem.
What Changes At This Difficulty
Stress-test transfer: multi-step structure, constraints, distractors, or reverse reasoning.
Expected structure: 3-4 step problem solving.
Vocabulary load: high with intentional distractors.
Reasoning depth: at least 3 relationship layers.
Student Work Signals
A good hard problem should expose the bottleneck
MathRoutine watches for whether the student understood the situation, wrote a useful setup, handled the calculation, and answered the exact question asked.
1
model hidden constraints or changed quantities
2
avoid tempting but incomplete first answers
3
explain why the final answer fits the original context
Sample Problems
A student needs at least 450 practice minutes this month. The student already has 165 minutes and plans to practice 35 minutes per day. How many more days are needed?
Reasoning strategy
Model the remaining minutes with a greater-than-or-equal inequality.
Why This Matters
The paid value is diagnosis, not answer lookup
Basic gives repeated targeted practice. Pro becomes useful when the student needs help understanding wording, recovering the setup, or seeing the same misconception return across attempts.
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