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Question Number 157972 by MathsFan last updated on 30/Oct/21

$$given2x=3yand4y=3z$$$$find\frac{3x-4y}{2x-y+5z}$$

Commented by tounghoungko last updated on 30/Oct/21

$$let3y=k\Rightarrow y=\frac{k}{3}\wedge 2x=k\Rightarrow x=\frac{k}{2}$$$$\Rightarrow z=\frac{4k}{9}$$$$\frac{\frac{3k}{2}-\frac{4k}{3}}{k-\frac{k}{3}+\frac{20k}{9}}=\frac{\frac{3}{2}-\frac{4}{3}}{\frac{2}{3}+\frac{20}{9}}=\frac{\frac{1}{6}}{\frac{26}{9}}=\frac{1}{6}\times \frac{9}{26}=\frac{3}{52}$$

Commented by MathsFan last updated on 30/Oct/21

$$thankssir$$

Commented by MathsFan last updated on 30/Oct/21

$$sir,howdidyougetz=\frac{4k}{3}$$

Commented by Rasheed.Sindhi last updated on 30/Oct/21

$$z=\frac{4}{3}y\Rightarrow z=\frac{4}{3}\times \frac{k}{3}=\frac{4k}{9}$$

Commented by MathsFan last updated on 30/Oct/21

$$yeah$$$$thanks$$

Commented by tounghoungko last updated on 30/Oct/21

$$givencodition3z=4yand3y=kory=\frac{k}{3}$$$$soz=\frac{4y}{3}=\frac{4}{3}\times \frac{k}{3}=\frac{4k}{9}$$

Answered by Rasheed.Sindhi last updated on 30/Oct/21

$$2x=3yand4y=3z;\frac{3x-4y}{2x-y+5z}=?$$$$2x=3y\Rightarrow \frac{x}{y}=\frac{3}{2}$$$$4y=3z\Rightarrow \frac{z}{y}=\frac{4}{3}$$$$\frac{3x-4y}{2x-y+5z}=\frac{3\left(\frac{x}{y}\right)-4}{2\left(\frac{x}{y}\right)-1+5\left(\frac{z}{y}\right)}$$$$=\frac{3\left(\frac{3}{2}\right)-4}{2\left(\frac{3}{2}\right)-1+5\left(\frac{4}{3}\right)}=\frac{\frac{9-8}{2}}{\frac{18-6+40}{6}}$$$$=\frac{1}{\cancel{\underset{1}{2}}}\times \frac{\cancel{\stackrel{3}{6}}}{52}=\frac{3}{52}$$

Commented by MathsFan last updated on 30/Oct/21

$$thankssir$$

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