When a question leaves an assumption open, state the assumption you use, solve with it, and say what changes if the other reading applies. Each answer is defensible when its assumption is stated.
This lesson is part of choosing a model from imperfect information. It continues from testing whether a model still works outside the data.
How do I write an answer with an open assumption?
Use a three-part frame: the assumption, the calculation, and the effect of the other reading.
- “I assume …” followed by the reading you choose.
- The calculation under that reading.
- “If instead …, the answer would be …”
Worked example: a taxi and a partial kilometre
A taxi charges RM1.50 for each kilometre. A trip is 7.3 km. The question does not say whether a partial kilometre is charged in full.
Model A (exact). Assume the charge is proportional to the exact distance. Cost = 1.50 × 7.3 = RM10.95.
Model B (rounded up). Assume each started kilometre is charged in full, so 7.3 km counts as 8 km. Cost = 1.50 × 8 = RM12.00.
Recommendation. Taxi meters in practice usually charge in steps, so Model B is the more realistic reading. The two answers differ by RM1.05, and the difference is part of the explanation.
Both models use the same rate and the same distance. Only the treatment of the partial kilometre differs, and that is the open assumption.
The mistake that costs marks
The common slip is to pick a reading silently. If the marker had the other reading in mind, the answer looks wrong with no explanation.
| Step | Wrong | Right |
|---|---|---|
| Reading chosen | exact, unstated | exact, stated as an assumption |
| Answer | RM10.95 | RM10.95 under exact charging |
| Other reading | not mentioned | RM12.00 if a started kilometre is charged in full |
| Marker’s view | answer differs from the key, no credit | assumption stated, partial credit likely |
Stating the assumption costs one sentence and protects the marks.
Check yourself
Mina reads a 240-page book at 35 pages per day. How many days does she need? State two defensible readings.
Answer
Dividing gives 240 ÷ 35 = 6.857 days.
Reading 1: count whole days. The last part of a day still takes a day, so she needs 7 days. This is the realistic reading for a reader who finishes on the seventh day.
Reading 2: use the exact number of days, about 6.9 days, for an average rate estimate.
The recommended answer is 7 days, with the assumption that she reads every day at the same rate.
What to study next
Test all four skills in the integrated practice set. For the general modelling sequence, return to defining variables and assumptions.
The algebra step repair trainer helps with the calculation in each model. For a teacher to help you word the assumption, see online one-to-one Mathematics tuition.