Question 593904: I am having trouble with the setup this question.
A food server examines the amount of money earned in tips after working an 8-hour shift. The server has a total of $191 in denominations of $1, $5, $10, and $20 bills. The total number of paper bills is 53. 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. Then use matrices to find the number of each denomination.
I have set up for the equations, where a =$1 bills, b=$5 bills, c=$10 bills and d=$20 bills
a + b + c + d =53
a + 5b +10c +20d =191
0 + b - 4c + 0 = 0 from the relationship b=4c
a - 2b + 0 + 0 = -1 from the relationship a=2b-1
I have tried solving it a couple of different ways, and I keep getting to a point that it doesn’t work. Do I have this set up correctly or am I missing something?
Answer by AnlytcPhil(1810)   (Show Source):
You can put this solution on YOUR website!
You have it set up correctly and the solution is
a = 31 ones
b = 16 fives
c = 4 tens
d = 2 twenties.
Keep working it. You're bound to get it if you don't
make a mistake.
Edwin
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