Word Problems: Translate Then Solve
Word problems feel hard when you jump to arithmetic before naming quantities. First define variables, write relationships in English, then convert to equations.
A translation playbook
Word problems feel hard when you jump to arithmetic before naming quantities. First define variables, write relationships in English, then convert to equations.
- "Is / equals / results in" → =
- "More than / total / sum" → +
- "Less than / difference" → − (order matters: "5 less than x" is x − 5)
- "Of / times / product" → ×
- "Per / each / rate" → often division or unit rate
Classic patterns
Age: relate present ages, then add/subtract years for past/future.
Money: price × quantity + price × quantity = total.
Distance: d = vt; if two travellers meet, sum of distances equals the gap.
Mixture: amount of pure ingredient = concentration × volume.
Capstone worked problem
A number increased by 20% becomes 84. Find the number.
Let the number be x. Then 1.2x = 84 → x = 84/1.2 = 70. Check: 20% of 70 is 14; 70+14=84. ✓
What to practise next
You now have arithmetic fluency, fractions/percents, algebra basics, graphs, and a word-problem process. Continue into the next lessons on data, integers depth, and measurement — then take Algebra & Precalculus on the learning path.
- Drill: 10 mixed linear equations daily until substitution feels automatic.
- Explain one solved problem out loud — teaching reveals gaps.
- When stuck, simplify numbers first, then restore the real values.