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Topic

Planning and Decision Making

Problem solving and decision making brings skills together so you can compare options, choose methods, and justify a practical decision.

Topic explanation

Applications problems often need more than one step. Break the context into smaller calculations and keep each answer labelled.

There may be extra information. Use only the values needed for the decision you are making.

A complete answer includes a clear conclusion. State which option is better, cheaper, faster, or more suitable, and give the evidence.

Quick methods

Read
Underline what the question is asking you to decide.
Plan
Choose the calculations needed before starting.
Compare
Use totals, differences, rates, or percentages as evidence.
Justify
Write a short final sentence with the decision and reason.

Worked examples

Group ticket decision

Four single tickets cost £6.00 each. A group ticket costs £21.00. Which is cheaper?

  1. Single tickets cost 4 × £6.00 = £24.00
  2. Compare £24.00 with £21.00.
  3. The group ticket is lower.

Answer: The group ticket is cheaper by £3.00.

Budget decision

A budget is £70.00. Food costs £18.00, travel £12.00, and entry £35.00. Is it within budget?

  1. Add costs: 18 + 12 + 35 = 65
  2. Compare £65.00 with £70.00.
  3. There is £5.00 left.

So: Yes, it is within budget by £5.00.

Yearly cost decision

Option A costs £25.00 per month. Option B costs £29.00 per month. Which is cheaper for a year, and by how much?

  1. Option A yearly cost: 25 × 12 = £300.00
  2. Option B yearly cost: 29 × 12 = £348.00
  3. Difference: 348 − 300 = £48.00

Final step: Option A is cheaper by £48.00.

Mixed decision

A class trip has a coach hire of £260 and entry costs £7.50 per pupil. There are 32 pupils. The budget is £520. Is the trip within budget?

  1. Entry cost = 32 × £7.50 = £240.00
  2. Total cost = £260.00 + £240.00 = £500.00
  3. Compare with the budget: £520.00 − £500.00 = £20.00

Answer: Yes. The trip is within budget by £20.00.

Watch out: Include both the fixed coach cost and the per-pupil entry cost before comparing with the budget.

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