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Math Help - AlgebraII Word Problem-Help

  1. #1
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    AlgebraII Word Problem-Help

    John was injured on the job and receievd a setllement of $1.5 million that he can live on for his retirement. John is going to pay off his debts(including his house) of $550,000. He is going to invest the balance in two accounts. One pays 7.5% and the other 4.5%. John will ONLY need $58,500 in order to live ar his current level.

    a. Write a system of equations that will help you determine the amount to be invested in each account.

    b. How much should John invest in each account in order to earn the $58,500 he needs?
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  2. #2
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    couple of assumptions here since they were not in the problem statement ...
    1. interest is simple interest per annum
    2. he needs $58,500 per year to support his present lifestyle

    $1.5 million - $550,000 = $950,000

    let x = amount of money invested at 7.5% interest
    then (950,000 - x) = amount of money invested at 4.5% interest

    interest earned = 58,500 = (x)(7.5%) + (950,000 - x)(4.5%)

    don't forget to change the percentages to decimals ... then solve for x.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by ep78 View Post
    John was injured on the job and receievd a setllement of $1.5 million that he can live on for his retirement. John is going to pay off his debts(including his house) of $550,000. He is going to invest the balance in two accounts. One pays 7.5% and the other 4.5%. John will ONLY need $58,500 in order to live ar his current level.

    a. Write a system of equations that will help you determine the amount to be invested in each account.

    b. How much should John invest in each account in order to earn the $58,500 he needs?
    Using a system of equations, it would look like this:

    Let x = amount invested at 7.5%
    Let y = amount invested at 4.5%
    Let $950,000 = total investment
    Let $58,500 = interest needed
    _____________________________
    x+y=950000

    .075x+.045y=58500
    _____________________________

    Solve the system
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