In a sale the price of a jacket is reduced by \(20\%\) to \(\$68\). Work out the original price of the jacket.
Question 1 Report
In a sale the price of a jacket is reduced by \(20\%\) to \(\$68\).
Work out the original price of the jacket.
Answer Details
This is a reverse percentage. The \(20\%\) was taken off the original price, so \(\$68\) represents \(100\% - 20\% = 80\%\) of the original, not \(100\%\).
If the original price is \(x\), then \(0.8x = 68\), so \(x = 68 \div 0.8\) [M1] oe.
Clear the decimal: \(\dfrac{68}{0.8} = \dfrac{680}{8} = 85\), so the original price was \(\$85\) [A1].
Check: \(20\%\) of \(\$85\) is \(\$17\), and \(85 - 17 = 68\), which matches the sale price.
Adding \(20\%\) to \(\$68\) gives \(\$81.60\), which is wrong because that percentage would be calculated on the reduced price rather than the original. When the value after a change is given, always divide by the multiplier.
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