Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\color{blue}{y=\frac{3}{40}xz}$
RECALL: When $y$ varies jointly as $x$ and $z$, the variation is represented by the equation $y=kxz$ where $k$ is the constant of variation. $y$ varies jointly as $x$ and $z$ so the equation of the variation is $y=kxz$ with $k$=constant of variation. To find the value of $k$, substitute the given values into $y=kxz$ to obtain: $$y=kxz \\\frac{3}{2}=k(2)(10) \\\frac{3}{2}=20k \\\dfrac{\frac{3}{2}}{20}=\frac{20k}{20} \\\frac{3}{2(20)}=k \\\frac{3}{40}=k$$ Thus, the equation of the variation is: $\color{blue}{y=\frac{3}{40}xz}$.