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# How to compare values using percentages

Percentages is a topic that many students struggle with in GCSE maths. But understanding how percentages work is one of those skills that will apply to your daily life above and beyond passing exams. Percentage discounts are a tactic often employed by retailers and it pays (excuse the pun) to know your stuff!

One of our tutors breaks down a sample question:

Question: Washing powder is sold in two sizes: Bag 1 is 600 grams for £3.30. Bag 2 is 1500 grams and usually costs £9.60 but currently has 15% off. Which is better value?

To determine which is better value, we need to determine the price per gram of each washing powder.

Bag 1: For the 600g bag, this is done by dividing the price by the number of grams: 3.30/600 = £0.0055/g or 0.55 pence/g.

Bag 2: For the second bag, we’ll first calculate the price including the discount. The full price (£9.60) is equal to 100%. We can therefore calculate the price per percent by dividing this by 100 (to get 0.096 or 9.6p). Now multiply this by 85 to determine how much this represents. This gives £8.16.

We’ll check to see if this value seems reasonable (using an estimation). It is especially important to do this when using a calculator and if using multiple units (£’s and pence).

Now calculate the price per gram for the second bag. As before, we divide the price by the number of grams: 8.16/1500 = £0.00544/g or 0.544 pence/g. We can check again now that the two results we have are of roughly the same order (not majorly different from each other). If they were very different (e.g. one is 10x another), we should go back and check the working once more for each, just in case.

The better value washing powder will have the lower price per gram, which in this case is bag 2. (If you’re answering a question like this in an exam, don’t forget to make a statement explaining your decision!)

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