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NSW Y8 Maths

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NSW Y8 Maths Rates and Ratios Ratio Word Problems

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Ratio Word Problems Theory

\begin{multicols}{2} \textbf{Example 1}\\ When making concrete, sand and cement are mixed together in the ratio \(4: 1\). If \(120 \text{~kg}\) of concrete is to be made, what weight of cement is required?\\ \textbf{Example 1 solution}\\ \(\begin{aligned} \text { Sand: cement } & =4: 1 \\ \text { Total parts } & =4+1 \\ & =5 \end{aligned}\)\\ \(\therefore 5\) parts of concrete \(=120 \text{~kg}\)\\ \(\begin{aligned} \therefore 1\text { part } & =120 \div 5 \\ & =24 \text{~kg} \end{aligned}\)\\ \(\therefore 24 \text{ kg}\) of cement are required. \columnbreak \textbf{Example 2}\\ Two numbers are respectively \(25 \%\) and \(50 \%\) more than a third number.\\ Find the ratio of the numbers\\ \textbf{Example 2 solution}\\ Let the third number be \(x\)\\ \(\begin{aligned} \therefore \text { First number } & =x+0.25 x \\ & =1.25 x \\ \text { Second number } & =x+0.5 x \\ & =1.5 x \end{aligned}\)\\ \(\begin{aligned} \therefore \text { Ratio 1st : 2nd :3rd} & =1.25 x: 1.5 x:x \\ & =1.25: 1.5 :1\\ & =\frac{125}{25}: \frac{150}{25}:\dfrac{100}{25} \\ & =5: 6:4 \end{aligned}\) \end{multicols}

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Videos relating to Ratio Word Problems.

  • Ratio Word Problems - Video - Ratio Word Problems 1

  • Ratio Word Problems - Video - Ratio Word Problems 2

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