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A bank teller is counting the total amount of money in a cash register at the end of the day. There is a total of \$2600 in denominations of \$1, \$5, \$10 and \$20 dollar bills.

The total number of paper bills is \$235. The number of twenty dollar bills is twice the number of \$1 dollar bills and the number of \$5 dollar bills is ten more than the number of \$1 dollar bills. What is the system of equations to represent the situation. Then use matrices to find the number of bills for each denomination.

Did you mean
" the total number of paper bills is 235" , not \$235 ?

let the number of \$1 bills be x
number of \$20 bills = 2x
number of \$5 bills = x+10
number of \$10 bills = y

x + 2x + x+10 + y = 235
4x + y = 225 (#1)

1(x) + 20(2x) + 5(x+10) + 10y = 2600
x + 40x + 5x + 50 + 10y = 2600
46x + 10y = 2550
23x + 5y = 1275 (#2)

Using matrices ???? , why?

from #1, y = 225-4x

sub into 2nd
23x + 5(225-x) = 1275
23x + 1125 - 5x = 1275
18x = 150
x = 150/18 ---> not a whole number,