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divide 72 in a ratio of 3:5

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The ratio is 3:5.
[tex]\frac{x}{y}=\frac{3}{5} \ \ \ |\hbox{cross multiply} \\ 5x=3y \ \ \ |\div 5 \\ x=\frac{3}{5}y[/tex]

You have to divide 72, so the sum of x and y is 72.
[tex]x+y=72 \ \ \ |-y \\ x=72-y[/tex]

Set both expressions equal to each other:
[tex]x=x \\ \frac{3}{5}y=72-y \ \ \ |\times 5 \\ 3y=360-5y \ \ \ |+5y \\ 8y=360 \ \ \ |\div 8 \\ y=45 \\ \\ x=72-y=72-45=27[/tex]

72 divided in a ratio of 3:5 is 27:45.
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