Math CentralQuandaries & Queries


Question from katie, a student:

i no many people have asked about this but im still unsure what is percentage change i have my ks3 tomorrow so please reply asap thankz

Hi Katie,

I am going to take a question we received a while ago and change the numbers and wording to ask this question.

The last week of March a car dealership sold 15 cars. A new sales promotion came out the first week of April and they sold 25 cars that week. What was the percent change in sales from the last week of March compared to the first week of April?

You want the change in the number of sales which is 25 - 15 = 10. Thus the dealership sold 10 more cars in the first week of April than it did in the last week of March. But you want to express this change as a percentage of the earlier value. The earlier value was 15 cars so the percentage change is

10/15 times 100 = 67%

You might also call this the percentage increase since there was an increase in the number of cars sold. So what if the number decreases? Here is another problem.

The last week of April a car dealership sold 20 cars. In the first week of May and they sold 18 cars. What was the percent change in sales from the last week of April compared to the first week of May?

Again it is the change, divided by the earlier value and then expressed as a percentage. Thus this time the percentage change is

(18 - 20)/20 times 100 = -10%

Hence there was a 10% decrease in sales from the last week in April to the first week in May.

I hope this helps,

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