Question

find a:b, if (3a+b):(a+b)=9:5​

Answer 1

Answer:

answer for the given problem is given

Answer 2

GIVEN :–

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• $\bf (3a+b):(a+b)=9:5$

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TO FIND :–

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• $\bf a:b =?$

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SOLUTION :–

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$\bf \implies (3a+b):(a+b)=9:5$

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$\bf \implies \dfrac{(3a+b)}{(a+b)}= \dfrac{9}{5}$

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• We should write this as –

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$\bf \implies \dfrac{(2a )+ (a+b)}{(a+b)}= \dfrac{9}{5}$

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$\bf \implies \dfrac{(2a )}{(a + b)} + \cancel\dfrac{(a+b)}{(a+b)}= \dfrac{9}{5}$

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$\bf \implies \dfrac{(2a )}{(a + b)} + 1= \dfrac{9}{5}$

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$\bf \implies \dfrac{(2a )}{(a + b)}= \dfrac{9}{5} - 1$

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$\bf \implies \dfrac{(2a )}{(a + b)}= \dfrac{9 - 5}{5}$

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$\bf \implies \dfrac{(2a )}{(a + b)}= \dfrac{4}{5}$

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$\bf \implies \dfrac{a}{a + b}= \dfrac{4}{5 \times 2}$

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$\bf \implies \dfrac{a}{a + b}= \dfrac{2}{5}$

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$\bf \implies \dfrac{a + b}{a}= \dfrac{5}{2}$

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$\bf \implies \cancel\dfrac{a}{a} +\dfrac{b}{a}= \dfrac{5}{2}$

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$\bf \implies 1 +\dfrac{b}{a}= \dfrac{5}{2}$

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$\bf \implies \dfrac{b}{a}= \dfrac{5}{2} - 1$

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$\bf \implies \dfrac{b}{a}= \dfrac{5 - 2}{2}$

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$\bf \implies \dfrac{b}{a}= \dfrac{3}{2}$

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$\bf \implies \dfrac{a}{b}= \dfrac{2}{3}$

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▪︎ Hence , $\bf \: \: \: \large{ \boxed{ \bf a:b=2:3}}$