Answer
A gallon of regular gasoline costs $1.82$, and premium costs $2.12$.
Work Step by Step
Let $x$ be the cost of a gallon of regular gasoline. Then the cost of a gallon of premium is $x+0.3$. Then our equation is: $14x+10(x+0.3)=46.68\\14x+10x+3=46.68\\24x=43.68\\x=1.82$
Thus a gallon of regular gasoline costs $1.82$, and premium costs $2.12$.
