[tex]\bf \textit{The sum of the two numbers is 80}\implies a+b=80
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\textit{the ratio of the two numbers is 3:5}\implies \cfrac{a}{b}=\cfrac{3}{5}\\\\
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a+b=80\implies \boxed{a=80-b}
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\cfrac{a}{b}=\cfrac{3}{5}\implies \cfrac{\boxed{80-b}}{b}=\cfrac{3}{5}\implies 5(80-b)=3b\implies 400-5b=3b
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400=8b\implies \cfrac{400}{8}=b\implies 50=b[/tex]
the larger ratio is the "5" one, thus that is the larger number.
