GCSE Maths Practice: best-value

Question 3 of 10

Different washing powder packs have different sizes and prices. Compare them carefully to find the best value.

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\( \begin{array}{l} \text{Washing powder offers:} \\ \text{A: 2 kg for £3.60} \\ \text{B: 1.5 kg for £2.40} \\ \text{C: 3 kg for £5.70} \\ \text{Which option gives the best value?} \end{array} \)

Choose one option:

Divide the total cost by the weight to compare value fairly.

Understanding Best Value by Weight

Best value questions often involve comparing products that come in different sizes and prices. In GCSE Maths, these problems are designed to test whether you can make fair comparisons rather than simply choosing the cheapest item. When products are sold by weight, such as washing powder, rice, or fruit, the fairest comparison is made by calculating the cost per kilogram.

Looking only at the total price can be misleading. A larger pack usually costs more, but that does not mean it is worse value. Similarly, a smaller pack may look cheaper but could cost more per kilogram. Unit pricing removes this confusion.

The Method: Cost per Kilogram

To find the best value when weight is involved, follow this method:

  1. Check that all weights are measured in kilograms. Convert grams to kilograms if needed.
  2. Divide the total price by the number of kilograms.
  3. Compare the costs per kilogram.

The option with the lowest cost per kilogram gives the best value.

Worked Example

A supermarket sells rice in three bags:

  • 2 kg for £3.20
  • 5 kg for £7.50
  • 1 kg for £1.80

Calculate the cost per kilogram:

  • £3.20 ÷ 2 = £1.60 per kg
  • £7.50 ÷ 5 = £1.50 per kg
  • £1.80 ÷ 1 = £1.80 per kg

Comparing these values shows which bag offers the lowest price per kilogram.

Another Example

Fruit is sold as:

  • 750 g for £1.35
  • 1.5 kg for £2.40
  • 3 kg for £5.10

First convert grams to kilograms, then divide the price by the weight to find the unit cost.

Common Mistakes

  • Not converting units: Always convert grams to kilograms before calculating.
  • Comparing total prices only: The cheapest pack overall is not always the best value.
  • Incorrect calculation: Divide price by weight, not weight by price.

Real-Life Applications

Cost-per-kilogram calculations are used every day in supermarkets. Shelf labels often show the unit price to help customers compare products quickly. This skill is also useful when budgeting, shopping in bulk, or comparing special offers.

Understanding best value helps you save money and avoid misleading deals.

Frequently Asked Questions

Do I always use cost per kilogram?
Yes, whenever products are sold by weight and the amounts differ.

What if weights are given in grams?
Convert them to kilograms first so all values are consistent.

Is this topic assessed in GCSE exams?
Yes. Best value by weight is common in Foundation exam papers.

Study Tip

If weights and prices are shown together, always calculate the unit price before choosing an answer.

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