Texts: A food server examines the amount of money earned in tips after working an 8-hour shift. The server has a total of $171 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 52. The number of $5 bills is 4 times the number of $10 bills, and the number of $1 bills is 1 less than twice the number of $5 bills. Write a system of linear equations to represent the situation. (Assume x = number of $1 bills, y = number of $5 bills, z = number of $10 bills, and w = number of $20 bills.)
Equation 1: x + y + z + w = 171
Equation 2: x + y + z + w = 52
Equation 3: y - z = 0
Equation 4: x - y = -1
Use matrices to find the number of each denomination.
x = $1 bill(s)
y = $5 bill(s)
z = $10 bill(s)
w = $20 bill(s)