Answer
Regular gas 4500gal, Performance Plus gas 500gal, and Premium gas 1500gal.
Work Step by Step
Step 1. Identify the quantities given in the Exercise: Regular gas price $p_1=3$ dollars/gal, Performance Plus gas price $p_2=3.2$ dollars/gal, and Premium gas price $p_3=3.3$ dollars/gal. Total gas sold is $G=6500$ gallons with a total of $S=20050$ dollars. Amount of Regular gas sold $G_1$ is three times of that of the Premium $G_1=3G_3$. (Here we assume the amounts sold for each gas are $G_1, G2, G3$)
Step 2: Establish equations based on the information given: income from the Regular gas is $S_1=p_1G_1=3G_1=9G_3$, income from the Performance Plus gas is $S_2=p_2G_2=3.2G_2$, and the income from the Premium gas is $S_3=p_3G_3=3.3G_3$
Step 3. The total gallons sold is $G=G_1+G2+G_3=G_2+4G_3=6500$, we have $G_2=6500-4G_3$.
Step 4. The total income equals to the sum of the above individual incomes, so we have $S_1+S_2+S_3=S$ and $9G_3+3.2(6500-4G_3)+3.3G_3=20050$
Step 5. Solve the above equation by combining like terms to get $0.5G_3=750$, $G_3=1500$ gallons and $G_1=3G_3=4500$ gallons, and $G_2=6500-4G_3=500$ gallons.
Step 6. We conclude that the sales are: Regular gas 4500gal, Performance Plus gas 500gal, and Premium gas 1500gal.
