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Question Number 150792 by mathdanisur last updated on 15/Aug/21

if ((y+z)/x) = ((10)/3) and (x/z) = (3/4) find (x/y) = ?

$$\mathrm{if}\:\:\:\frac{\mathrm{y}+\mathrm{z}}{\mathrm{x}}\:=\:\frac{\mathrm{10}}{\mathrm{3}}\:\:\mathrm{and}\:\:\frac{\mathrm{x}}{\mathrm{z}}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\:\frac{\mathrm{x}}{\mathrm{y}}\:=\:? \\ $$

Answered by nimnim last updated on 15/Aug/21

y=((10x−3z)/3) and 3z=4x ∴(x/y)=(x/((10x−4x)/3)) =(1/2)

$${y}=\frac{\mathrm{10}{x}−\mathrm{3}{z}}{\mathrm{3}}\:\:\:\:{and}\:\:\:\:\mathrm{3}{z}=\mathrm{4}{x} \\ $$$$\therefore\frac{{x}}{{y}}=\frac{{x}}{\frac{\mathrm{10}{x}−\mathrm{4}{x}}{\mathrm{3}}}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Commented by mathdanisur last updated on 15/Aug/21

Thankyou Ser

$$\mathrm{Thankyou}\:\mathrm{Ser} \\ $$

Answered by Rasheed.Sindhi last updated on 15/Aug/21

((y+z)/x) = ((10)/3) and (x/z) = (3/4);(x/y) = ? (y/x)+(z/x)=((10)/3) (y/x)+(4/3)=((10)/3) [ ∵ (x/z) = (3/4)⇒(z/x)=(4/3)] (y/x)=((10)/3)−(4/3)=(6/3)=2 (x/y)=(1/2)

$$\:\:\:\:\frac{\mathrm{y}+\mathrm{z}}{\mathrm{x}}\:=\:\frac{\mathrm{10}}{\mathrm{3}}\:\:\mathrm{and}\:\:\frac{\mathrm{x}}{\mathrm{z}}\:=\:\frac{\mathrm{3}}{\mathrm{4}};\frac{\mathrm{x}}{\mathrm{y}}\:=\:? \\ $$$$\frac{\mathrm{y}}{\mathrm{x}}+\frac{\mathrm{z}}{\mathrm{x}}=\frac{\mathrm{10}}{\mathrm{3}}\:\: \\ $$$$\frac{\mathrm{y}}{\mathrm{x}}+\frac{\mathrm{4}}{\mathrm{3}}=\frac{\mathrm{10}}{\mathrm{3}}\:\:\left[\:\because\:\frac{\mathrm{x}}{\mathrm{z}}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\Rightarrow\frac{\mathrm{z}}{\mathrm{x}}=\frac{\mathrm{4}}{\mathrm{3}}\right] \\ $$$$\frac{\mathrm{y}}{\mathrm{x}}=\frac{\mathrm{10}}{\mathrm{3}}−\frac{\mathrm{4}}{\mathrm{3}}=\frac{\mathrm{6}}{\mathrm{3}}=\mathrm{2} \\ $$$$\frac{\mathrm{x}}{\mathrm{y}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Commented by mathdanisur last updated on 15/Aug/21

thank you Ser

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{Ser} \\ $$

Answered by maged last updated on 15/Aug/21

(y/x)+(z/x)=((10)/3)⇒(y/x)+(4/3)=((10)/3)⇒(y/x)=(6/3) ⇒(x/y)=(1/2)

$$\frac{\mathrm{y}}{\mathrm{x}}+\frac{\mathrm{z}}{\mathrm{x}}=\frac{\mathrm{10}}{\mathrm{3}}\Rightarrow\frac{\mathrm{y}}{\mathrm{x}}+\frac{\mathrm{4}}{\mathrm{3}}=\frac{\mathrm{10}}{\mathrm{3}}\Rightarrow\frac{\mathrm{y}}{\mathrm{x}}=\frac{\mathrm{6}}{\mathrm{3}} \\ $$$$\Rightarrow\frac{\mathrm{x}}{\mathrm{y}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

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