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Succeed with maths: part 1

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# 2.3 Calculating original amounts

A situation that can be a little tricky to understand is how to undo a percentage change that has been added to or subtracted from a number. The video below will show how to work this out, again using an example with discounts and VAT.

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From the video, you can check your answer by working out the 5 per cent postage charge on £28.57 to see that the grand total will be £30.

Many people in this situation may think that they can work out 5 per cent of £30 and subtract this from the £30 to find out how much they can spend. Try this now.

5% of £30 = 0.05 × £30 = £1.50

£30 – £1.50 = £28.50

This answer is 7p less than using our other method! So something must be wrong.

The reason for this is because this is all to do with what it’s 5% of! 5% of different numbers gives a different answer. The 5% added here is 5% of £28.57. 5% of £30 isn’t the same as 5% of £28.57 – it’s a bigger number.

This is an important idea to remember. Have a go at this in the next two activities.

## Activity 7 What was the price before VAT?

Timing: Allow approximately 10 minutes

The price of a tennis racquet, including 20 per cent VAT, is £45.24. What was the price before VAT?

Hint: the £45.24 includes VAT. What percentage does this total represent? Find the monetary amount that represents 1 per cent, and use that figure to arrive at 100 per cent.

The price before VAT was added is the original 100 per cent.

So £45.22, which includes VAT, is equivalent to 120 per cent of the cost (100% + 20%).

1 per cent of £45.24 = £45.24 ÷ 120

Thus, the price of the tennis racquet before VAT was applied was £37.70.

## Activity 8 What was the original price before a sale?

Timing: Allow approximately 10 minutes

I saw a coat in a sale. Its sale price was advertised as £64, which was after a 20% discount.

Unfortunately, I wasn’t able to buy it in the sale – the sale was ending soon and I’d not yet been paid that month.

However, as I really liked the coat, I thought I might buy it anyway at full price once I’d been paid. How much would it cost me when not in the sale?