Math CentralQuandaries & Queries


Question from Meghan, a student:

Pace Design's sales increased by 30% in the first year, increased by 60% in the second year, decreased by 60% in the third year and increased by 90% in the fourth year. What was the cumulative change in sales over the 4 years?

Hi Meghan,

A friend of mine knits wool hats for the cold winters here in Saskatchewan and sells them at a local craft store. In the winter of 2008/09 she sold $N$ hats. In the winter of 2009/10 she had a $20\%$ increase in sales so she sold $N \times 1.2$ hats in the winter of 2009/10. Sales increased again the following year, this time by $30\%$ and hence in 2010/11 she sold $(N \times 1.2) \times 1.3 = N \times 1.56$ hats. The winter of 2011/12 was especially warm and she didn't sell as many hats, in fact the sales decreased by $40\%$ and hence she only sold $60\%$ of what she sold in the previous year. Thus her sales in 2011/12 were $((N \times 1.2) \times 1.3) \times 0.60 = N \times 0.936$ hats.

This winter in cold so I expect her sales will increase again but it is too early to tell.


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