1. At a certain gas station, a total of 500 gallons of gas was sold on a particular day. Regular gas (x) sells for $2.25 per gallon. Premium gas (y) sells for $3.00 per gallon. The total gas receipts for the day was $1,233.75.
(a) Write an equation in x and y for the number of gallons of gas sold.
(b) Write an equation in x and y for the amount of money received.
(c) Write the augmented matrix for (a) and (b).
(d) Solve for x and y using the augmented equation and Gaussian elimination. Annotate each step you take to get to your answer.
(e) Verify that your answer is correct by putting x and y into the equations you derived in (a) and (b).