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NSW Y8 Maths

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NSW Y8 Maths Fractions and Percentages The Unitary Method

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The Unitary Method Theory

\begin{multicols}{2} \textbf{Example 1}\\ Alice buys a dress that has been discounted by \(30 \%\). If the sale price is \(\$ 63\), what was the original price of the dress?\\ \textbf{Example 1 solution}\\ \(30 \%\) discount then \(70 \%\) of the original price is the discounted price.\\ \(\begin{aligned} \therefore 70 \% \text { of original price } & =\$ 63 \end{aligned}\)\\ \(\begin{aligned} 1 \% \text { of origins price } & =\$ 63 \div 70 \\ & =0.90 \end{aligned}\)\\ \(\begin{aligned} \therefore 100 \% \text { of origin price } & =0.90+100 \\ & =\$ 90 \end{aligned}\)\\ \(\begin{aligned} \therefore \text { original price }= & \$ 90 . \end{aligned}\) \columnbreak \textbf{Example 2}\\ There were 20119 men in the crowd at a tennis match. If this is \(55 \%\) of the crowd, what was the total attendance?\\ \textbf{Example 2 solution}\\ Let \(t=\) total attendance\\ \(\begin{aligned} \therefore 55 \% \times t & =20119 \\ 1 \% \times t & =20119 \div 55 \\ & =365.8 \\ 100 \% \times t & =365.8 \times 100 \\ \therefore t & =36580 \end{aligned}\)\\ \(\therefore\) Total attendance is 36580. \end{multicols}

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