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MathidiaMathematics Academy
Financial mathematics and modelling
Lesson 73 of 75
Standard practice

Tariffs and best value

Objective. Compare fixed charges and variable rates.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Comparing tariffs and best value means working out the total cost of different pricing plans, each usually combining a fixed charge with a variable rate depending on usage, to see which option is cheaper for a given amount of use. The method is to write a total cost formula for each tariff, such as total = fixed charge + (rate × units used), then substitute the same usage figure into each formula to compare the results directly. For example, comparing a tariff charging £10 plus 5p per unit against one charging £20 plus 2p per unit requires calculating both totals at a specific usage level, such as 500 units, to see which is cheaper. The tariff that gives the lower total cost for the required amount of usage represents the best value.

Worked example

Tariff A costs £15 plus 4p per unit. Tariff B costs £25 plus 2p per unit. Find which tariff is better value for 600 units used.

£15.00
Money illustration for £15
  1. 1Calculate Tariff A's total: £15 + (0.04 × 600) = 15 + 24 = £39.
  2. 2Calculate Tariff B's total: £25 + (0.02 × 600) = 25 + 12 = £37.
  3. 3Compare the two totals: £39 versus £37.
  4. 4Since £37 is lower, Tariff B gives better value for 600 units.

Answer: Tariff B is better value, costing £37 compared to £39 for Tariff A.

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Common mistake. Pupils sometimes compare only the fixed charges or only the variable rates between tariffs, rather than calculating the full total cost at a specific usage level. Always substitute the same usage amount into both complete cost formulas before comparing.

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