problem: Eight pounds of feathers and two ounces of gold together cost $\$932$. Fourteen pounds of feathers and three ounces of gold together cost $\$1402$. What is the cost of five pounds of feathers and five ounces of gold?
solution: Let $f$ be the cost of a pound of feathers and $g$ the cost of an ounce of gold.  We have \begin{align*}
  8f+2g&=932 \\
  14f+3g&=1402
  \end{align*}Solving the first equation for $g$ we get $g=466-4f$.  Substituting into the second equation, we solve \[
  14f+3(466-4f)=1402
  \]to find $f=2$.  Substituting into $g=466-4f$ we have $g=458$.  Thus five pounds of feathers and five ounces of gold costs $5(f+g)=\boxed{2300}$ dollars.