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Best Buys

FoundationHigherAQAEdexcelOCR

Practise best buys with this free Foundation and Higher GCSE Maths worksheet from Virtus Academy. You'll work through comparing best buys and value for money, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. Work out the price per unit to compare which option is genuinely cheaper.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Best buy questions compare two or more options and ask which gives better value. The reliable method is to find a common basis for comparison, usually the cost of one unit.

There are two ways to do this: the price per unit, or the amount per pound. Either works, but you must be clear which you have calculated, because they point in opposite directions. A lower price per gram is better value, whereas a higher number of grams per pound is better value.

Exam answers need a conclusion, not just numbers. State which option is the better buy and support it with the figures you worked out, since the mark is usually for the comparison rather than the arithmetic.

Revision notes

Price per unit

Divide the cost by the quantity to find what one unit costs. The lower figure is the better buy.

A \(500\)g pack at \(£2.20\) costs \(2.20 \div 500 = £0.0044\) per gram. Working in pence often avoids awkward decimals: \(220 \div 500 = 0.44\)p per gram.

Quantity per pound

Divide the quantity by the cost to find how much you get for \(£1\). Here the higher figure is better value.

The same pack gives \(500 \div 2.20 = 227\)g per pound. Both methods reach the same conclusion, so choose whichever gives tidier numbers.

Scaling to a common amount

Sometimes the neatest approach is to scale both options to the same quantity.

If one pack is \(300\)g and another \(900\)g, multiply the smaller by \(3\) and compare directly. This works well when the quantities are simple multiples.

Key points

  • Find a common basis for comparison.
  • Price per unit: lower is better.
  • Quantity per pound: higher is better.
  • Work in pence to avoid awkward decimals.
  • Both methods give the same conclusion.
  • Always state which option is the better buy.

Worked examples

Example 1

A \(400\)g jar costs \(£1.60\) and a \(600\)g jar costs \(£2.28\). Which is better value?

Working

\[160 \div 400 = 0.4\text{p per g}\]find the price per gram for the first jar
\[228 \div 600 = 0.38\text{p per g}\]find the price per gram for the second
\[\text{The 600g jar is better value}\]the lower price per gram wins

Example 2

Pack A: \(6\) cans for \(£3.60\). Pack B: \(10\) cans for \(£5.50\). Which is cheaper per can?

Working

\[360 \div 6 = 60\text{p per can}\]find the cost per can for pack A
\[550 \div 10 = 55\text{p per can}\]find the cost per can for pack B
\[\text{Pack B is cheaper per can}\]state the conclusion

Example 3

A \(250\)ml bottle costs \(£1.20\) and a \(750\)ml bottle costs \(£3.30\). Compare by scaling.

Working

\[250\text{ml} \times 3 = 750\text{ml}\]scale the smaller bottle to match the larger
\[£1.20 \times 3 = £3.60\]three small bottles would cost £3.60
\[\text{The 750ml bottle is better value}\]it costs less than £3.60 for the same volume

Common mistakes

  • Comparing prices without comparing quantities.

    A bigger pack costing more is not automatically worse value. Reduce both to a common unit.

  • Mixing up the two methods.

    Lower is better for price per unit, but higher is better for quantity per pound. Be clear which you calculated.

  • Not stating a conclusion.

    The mark is for saying which is the better buy, not just for the two divisions.

  • Mixing pounds and pence.

    Work consistently in one unit, usually pence, to avoid factor-of-100 errors.

Exam tips

  • Work in pence to keep the numbers tidy.
  • Say clearly whether you found price per unit or quantity per pound.
  • Always finish with a sentence naming the better buy.
  • Keep enough decimal places to distinguish close options.

Key terms

Unit price
The cost of one unit of a product.
Value for money
How much you get for each pound spent.
Better buy
The option giving more product per pound.
Proportion
The relationship between quantity and price.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.