# Video: AQA GCSE Mathematics Higher Tier Pack 1 • Paper 3 • Question 18

AQA GCSE Mathematics Higher Tier Pack 1 • Paper 3 • Question 18

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### Video Transcript

A food stall is selling a jumbo deluxe hot dog for six pounds 25. At the end of the day, the food stall drops the price to three pounds 99. Work out the percentage decrease in the price of a jumbo deluxe hot dog.

There’s a formula that we can use to help us calculate a percentage decrease. We first find the difference between the two amounts and then divide it by the original. This will give a decimal. And so to convert this to percentage, we then multiply by 100. There is a common mistake which we need to watch out for. Often what some students will do is just divide by the smaller of the two numbers. But our formula tells us that we must divide by the original regardless of whether that’s smaller or larger.

In fact in this case, where we’re calculating a percentage decrease, the original amount will actually be the larger of the two numbers. Let’s apply this formula with our numbers. The difference between the two prices will be the price at the start of the day minus the price at the end of the day. So that’s six pounds 25 minus three pounds 99. We then divide by the original price, so that’s six pound 25. This calculation will give a decimal, so finally to convert to a percentage, we multiply it by 100.

We could take this calculation into our calculator exactly as it appears, or we can work it out in stages. 6.25 minus 3.99 is 2.26. So we have 2.26 over 6.25 multiplied by 100. 2.26 divided by 6.25 is 0.3616, and multiplying by 100 gives 36.16. There’s no need to round the answer. So we conclude that the percentage decrease in the price of a jumbo deluxe hot dog is 36.16 percent.