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.
01A 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
02Classic 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.
03Capstone 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. ✓
04What 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.