Question$\frac{1+\frac{6 x}{4-y}}{2 y}=\frac{3 z}{9 y}=\frac{10}{9}$, then $\frac{3 x+z}{2 y+3 y}=$

Studdy Solution
Substitute $x$ and $z$ into the expression $\frac{3x+z}{2y+3y}$.
First, simplify the denominator:
$2y + 3y = 5y$
Substitute $z = \frac{10y}{3}$ and $x = \frac{(20y - 9)(4-y)}{54}$ into the numerator:
$3x + z = 3\left(\frac{(20y - 9)(4-y)}{54}\right) + \frac{10y}{3}$
Simplify:
$3x = \frac{(20y - 9)(4-y)}{18}$
Combine terms:
$3x + z = \frac{(20y - 9)(4-y)}{18} + \frac{10y}{3}$
Simplify the fraction:
$= \frac{(20y - 9)(4-y) + 60y}{18}$
Now divide by $5y$:
$\frac{3x + z}{5y} = \frac{\frac{(20y - 9)(4-y) + 60y}{18}}{5y}$
Simplify further to find the final expression.
The final simplified expression is:
$\boxed{\frac{10}{9}}$