Question

If $4x=3y$, what is the value of $\frac{2x+y}{3x-2y}$?

Answer 1

Answer:

10

Step-by-step explanation:

Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\

&=

\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\

&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}