Question

LINEAR ALGEBRA please show neatly work and correct answers in correct order shown!!

A food server examines the amount of money earned in tips after working an 8-hour shift. The server has a total of $95 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 26. 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.) Y + Z + W95 z + 26 Use matrices to find the number of each denomination. $1 bill(s) $5 bill(s) 10 bill(s) $20 bill(s) WE

Answer 1

All answers are in closed boxes..

Any doubt in any step then comment below..

x = no of $1 bills y = no of $5 bills z = no of $10 bills w = no of $20 bills x + 5y + 10z + 20w = 95 x + y + z + w = 26 total no of bills y = 4z y - 4z = 0 x = 2y - 1 x - 2y = -1 [1 1 0 1 5 1 1 -2 10 1 -4 0 20 1 0 0] [x y z w] = [95 26 0 -1] \r\n Augmented matrix (A: B] gives [1 1 0 1 5 1 1 -2 10 1 -4 0 20 1 0 0 95 26 0 -1] R_2 rightarrow R_2 - R_1 R_4 rightarrow R_4 - R_1 [1 0 0 0 5 -4 -1 -7 10 -9 -4 -10 20 -19 0 -20 95 -69 0 -96] similarly, do this, we get