Pre Calculus

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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.

  • Pre Calculus -

    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.

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