A repair company charges a $42 visit fee plus $18 per hour. The bill was $150. How many hours did the repair take?
Reasoning strategy
Write 42 + 18h = 150 and solve for h.
Difficulty Practice Guide
Hard Grade 8 Linear Equations Word Problems
This page shows what hard practice should demand for grade 8 linear equations 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 has 18 solved problems and plans to solve the same number each day. After 6 days, the student has 72 solved problems. How many problems were solved each day?
Reasoning strategy
Model the starting amount plus 6 equal daily amounts.
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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