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AQA GCSE · Question 05 · Algebra
The total cost of a taxi ride is calculated by adding a fixed charge of £4 and a charge of £2 per mile. Write a formula to work out the total cost, £C, of a journey of m miles.
The total cost of a taxi ride is calculated by adding a fixed charge of £4 and a charge of £2 per mile. Write a formula to work out the total cost, £C, of a journey of m miles.
How to approach this question
1. Identify the variables: C for total cost and m for the number of miles.
2. Identify the fixed part of the cost, which does not change with the number of miles.
3. Identify the variable part of the cost, which depends on the number of miles.
4. Combine the fixed and variable parts to form the formula for C.
Full Answer
C = 4 + 2m
The problem describes how to calculate the total cost, C. We need to translate this description into a mathematical formula.
The cost has two components:
1. A fixed charge of £4. This amount is paid regardless of the distance.
2. A charge of £2 per mile. This amount depends on the number of miles, m. For m miles, this charge is 2 × m, or 2m.
The total cost, C, is the sum of these two components.
Total Cost = Fixed Charge + (Charge per mile × Number of miles)
C = 4 + 2m
Common mistakes
✗ Writing 4m + 2 (mixing up the fixed and variable charges).
✗ Writing C = 4 + 2, forgetting the variable m.
✗ Writing an expression (4 + 2m) instead of a formula (C = 4 + 2m).
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