Before you calculate a fare, write the pricing rule in words and list only the quantities that rule uses. Everything else in the question is extra.
This lesson is part of choosing a model from imperfect information. It applies the opening lines from defining variables and assumptions.
How do I sort the numbers in a question?
Read the question once for the pricing rule and once for the values. Label every value as needed, extra or missing.
- Write the rule in words, for example “base fare plus a charge per km plus a charge per minute”.
- Match each value in the question to a part of the rule.
- Mark values that match nothing as extra.
- Mark parts of the rule with no value as missing.
Worked example: an e-hailing fare
A trip costs RM3 as a base fare, RM1.20 for each kilometre and RM0.30 for each minute. Nadia takes a trip of 12 km that lasts 25 minutes. The driver is named Faiz, the car is silver, and two passengers ride together.
Step 1. The rule in words: base fare plus km charge plus minute charge.
Step 2. Match the values. The RM3, RM1.20 and RM0.30 are rates. The 12 km and the 25 minutes are the quantities.
Step 3. The driver’s name, the car colour and the number of passengers match nothing. They are extra.
Step 4. Calculate: fare = 3 + 1.20 × 12 + 0.30 × 25 = 3 + 14.40 + 7.50 = RM24.90.
Sorting took two lines, and it stopped any attempt to divide by the two passengers.
The mistake that costs marks
The common slip is using a number because it is there. Dividing the fare by 2 for two passengers gives RM12.45 each, but the question asked for the fare.
| Step | Wrong | Right |
|---|---|---|
| Fare | RM24.90 | RM24.90 |
| Extra detail | passengers used: 24.90 ÷ 2 | passengers ignored |
| Answer | RM12.45 | RM24.90 |
| Reason | “the question mentions 2” | the question asks for the fare of the trip |
Ask what the question wants before deciding what to use.
Check yourself
A courier charges RM6 for the first kilogram and RM2.50 for each extra kilogram. A parcel weighs 5 kg. The sender is 15 years old and lives 30 km away. Find the charge.
Answer
The rule in words is the first-kilogram charge plus the extra-kilogram rate times the extra kilograms. The sender’s age and the distance match nothing in the rule, so they are extra.
Extra kilograms: 5 − 1 = 4. Charge: 6 + 2.50 × 4 = 6 + 10 = RM16.
What to study next
Go on to comparing a fixed fee and a usage fee with an explicit break-even point. When you want mixed questions, try the integrated practice set.
The algebra step repair trainer helps with the calculation step. For a teacher to watch you sort a question, see online one-to-one Mathematics tuition.