1. A food server examines the amount of money earned in tips after working an 8-hour shift. The server has a total of $102 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 24. The number of $1 bills is four times the number of $10 bills, and the number of $5 bills is two more than twice the number of $10 bills.
a) Write a system of linear equations to represent the situation, where $x_1$, $x_2$, $x_3$, and $x_4$ represent the numbers of $1 bills, $5 bills, $10 bills, and $20 bills respectively. (2 pts)
b) Use an augmented matrix and Gaussian elimination to find the number of each type of bill the server received in tips. (8 pts)