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Equal percentage increase and decrease

Equal percentage increase and decrease

IP 1
7 marks
  1. The price of a \(\$200\) bag is increased by \(25\%\) and the new price is then decreased by \(25\%\). Find the final price.[1]
  2. A price is increased by \(x\%\) and the new price is then decreased by \(x\%\), where \(0<x<100\). Show that the final price is \(\left(1-\dfrac{x^2}{10\,000}\right)\) of the original price, and explain why it is always lower than the original.[3]
  3. Does the final price change if the decrease is made first? Explain.[1]
  4. Find \(x\) if the final price is \(4\%\) lower than the original price.[2]

Solution:

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Answer:(a) \(187.50\) dollars (b) multiplier \(\left(1+\dfrac{x}{100}\right)\left(1-\dfrac{x}{100}\right)=1-\dfrac{x^2}{10\,000}<1\) (c) no: multiplication order does not matter (d) \(x=20\)

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