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Posted by on Thursday, July 28, 2011 at 11:54pm.

To buy both a new car and a new house, Tina sought two loans totalling $78,825. The simple interest rate on the first loan was 0.2%, while the simple interest rate on the second loan was 5.0%. At the end of the first year, Tina paid a combined interest payment of $2817.23. What were the amounts of the two loans?

  • Intermediate Algebra - , Friday, July 29, 2011 at 2:13am

    Let the two loan amounts be X and Y.

    X + Y = 78,825
    0.002X + 0.05Y = 2817.23

    Solve those two simultaneous equations.
    Multiply both sides of the second equation by 20.

    0.04x + Y = 56,344.60

    0.96 X = 22,480.40
    X = 23,417.08
    Y = 55,407.92

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