Math CentralQuandaries & Queries


Question from Carol:

I bought a computer for £330.
The selling price included VAT at 20%.
Then I was allowed a staff discount of £30.
What was it’s original price before the VAT and staff discount?

Hi Carol,

Think about the process going forward. You see a computer and notice its original price. Then you have to add 20% to this to get the price including the VAT. Finally you discount this price by 30% and reach the purchase price of £330. Now write this process mathematically.

Suppose the original price is £x. The price including VAT is $£x + 0.2 \times £x = 1.2 \times £x.$ You get to discount this price by 30% so you only need to pay 100% - 30% = 70%. Thus what you pay is $0.70 \times 1.2 \times £x.$ this amount is £330. Solve for x.

Once you know the original price check you answer by going forward. Add 20% and apply a 30% discount to ensure you get £330.


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