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Determining quantities from ratios

We show by examples how to determine quantities from ratios.

  • Finding one quantity from the other. In a class with a ratio of boys to girls of $$\Tblue{2}:\Tgreen{3}$$, there are $$\Tblue{12}$$ boys. The number of girls is $$ \frac{\Tblue{12}}{\Tblue{2}}\times\Tgreen{3}= 6\times\Tgreen{3} = \Tgreen{18}. $$
  • Splitting quantities. There are $$\Torange{45}$$ pupils in the class. The proportion of boys is $$\displaystyle\frac{\Tblue{2}}{\Tblue{2}+\Tgreen{3}} = \frac{\Tblue{2}}{\Torange{5}}$$. The number of boys is $$ \frac{\Torange{45}}{\Torange{5}}\times\Tblue{2} = 9\times\Tblue{2} = \Tblue{18}.$$
  • Ratio with more than two numbers. A sum of $$\Torange{20}$$ euros is to be split between John, Mark and Paul in a ratio $$\Tblue{2}:\Tgreen{7}:\Tviolet{1}$$. They will receive in euros \begin{align*} &\frac{\Torange{20}}{\Tblue{2}+\Tgreen{7}+\Tviolet{1}}\times\Tblue{2} = \frac{\Torange{20}}{\Torange{10}}\times\Tblue{2} = 20\times\Tblue{2} =\Tblue{40},\\ &\quad\frac{\Torange{20}}{\Torange{10}}\times\Tgreen{7} = \Tgreen{140},\quad \frac{\Torange{20}}{\Torange{10}}\times\Tviolet{1} = \Tviolet{20}. \end{align*}