Chapter 5, Systems of Equations and Inequalities - Section 5.2 - Systems of Linear Equations in Several Variables - 5.3 Exercises - Page 456: 42

$x=4500,$ $y=500,$ $z=1500$

Let $x$ denote regular gas Let $y$ denote performance plus Let $z$ denote premium Thus, $x+y+z=6500$ and $3x+3.2y+3.3z=20050$. Since $x=3z$. Multiplying Equation 1 by -3.2 and adding it to Equation 2. $\begin{cases} -3.2y-12.8z=-20800\\ 3.2y+12.3z=20050\\ -- -- -- -- --\\ -0.5z=-750 \end{cases}$ Thus, $z=1500$. Since $x=3z, x=4500$. $y=500$