Pre Calculus
posted by Jona on .
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.

X $1 Bills.
2x $20 Bills.
(X+10) $5 Bills.
Y $10 Bills.
x + 2x + (x+10) + y = 235
4x + 10 + y = 235
Eq1: 4x + y = 225.
1*x + 20*2x + 5(x+10) + 10y = $2600.
46x+50+10y = 2600.
Eq2: 46x+10y = 2550
40x  10y = 2250
46x + 10y = 2550
6x = 300.
X = 50.
2X = 100
X+10 = 60
4*50 + y = 225
Y = 25.
The student should solve Eq1 and Eq2 using matrix and get the same results.