Costs from a Calculated Value

Video coming soon3 worked examples

Theory

Many Applications questions are two jobs in one: first calculate a quantity (an area, a volume, a distance or a number of items), then use it to work out a cost. The marks are split across both stages, so the measurement work matters as much as the money.

1. The Two-Stage Method

Stage 1: work out the quantity needed — area of a floor, volume of a tank, litres of fuel, number of packs.
Stage 2: multiply by the price per unit, or divide to find how many units are needed and then cost them.

\text{Total Cost} = \text{Quantity} \times \text{Cost per Unit}

2. Buying in Whole Units

Materials are usually sold in whole packs, tins or rolls. If the calculation gives 7.2 tins, you cannot buy 0.2 of a tin — you must round up to 8 and cost 8. This is the opposite of normal rounding, and it is where most marks are lost.

3. Comparing Options

If asked whether a job comes in under budget, or which supplier is cheaper, calculate the full cost of each and finish with a written comparison against the figure given.

The Golden Rule: check the units match the price before costing. If covering is priced per square metre, the area must be in m² — not cm². Then, if the item is sold in whole units, always round up.

⚠️ Common Examiner Traps

Rounding down: 7.2 tins of paint means 8 tins must be bought. Rounding to 7 leaves the job unfinished.
Mismatched units: an area worked out in cm² cannot be costed at a price per m² — convert first ( $1\ \text{m}^2 = 10{,}000\ \text{cm}^2$ ).
Forgetting the second stage: the question asks for a cost; stopping at the area or volume leaves marks behind.
No conclusion: if asked "is it within budget?", state clearly whether it is, and by how much.

Worked examples

Example 1

Area then Cost

A rectangular function room measures 12 m by 7.5 m. New carpet costs £18.50 per square metre. Calculate the cost of carpeting the room.

Step 1: Calculate the area. The measurements are already in metres, matching the price:

12 \times 7.5 = 90\ \text{m}^2

Step 2: Multiply by the cost per square metre:

90 \times 18.50 = 1665

Answer: the carpet costs £1665.00.

Example 2

Rounding Up to Whole Units

A wall has an area of 46 m². One tin of paint covers 12 m² and costs £21.95. Calculate the cost of the paint needed.

Step 1: Work out how many tins are needed:

46 \div 12 = 3.83\ldots

Step 2: You cannot buy part of a tin, and 3 tins would not cover the wall — so round up to 4 tins.

Step 3: Cost the whole tins:

4 \times 21.95 = 87.80

Answer: the paint costs £87.80.

Example 3

🎯 Exam-style (within budget?)

A path 15 m long and 2 m wide is to be laid with gravel. Gravel is sold in bags covering 5 m² each, costing £8.40 a bag. The budget for the job is £50. Determine whether the job can be done within budget.

Step 1: Calculate the area of the path:

15 \times 2 = 30\ \text{m}^2

Step 2: Work out the bags needed and round up if necessary:

30 \div 5 = 6 \text{ bags}

Step 3: Cost the bags:

6 \times 8.40 = 50.40

Step 4: Compare with the budget and state a conclusion.

Answer: No — the job cannot be done within budget, as £50.40 exceeds the £50 available (by 40p).

Ready to practise?

9 Costs from Measurements questions with answers and video solutions