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Math Help - Confusing Word Problem

  1. #1
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    Confusing Word Problem

    If anyone could me figure out this problem I would greatly appreciate it. I think I started right but I'm a little lost.

    Cole's two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed $1024.40 in interest. What was the amount of each loan?

    Thanks in advance,
    Picturelady
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  2. #2
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    Quote Originally Posted by picturelady View Post
    If anyone could me figure out this problem I would greatly appreciate it. I think I started right but I'm a little lost.

    Cole's two student loans totaled $31,000. One of his loans was at 2.8% simple interest and the other at 4.5%. After one year, Cole owed $1024.40 in interest. What was the amount of each loan?

    Thanks in advance,
    Picturelady
    ++++++++++++++++++++++++++++++++++
    Let ( X )be the loan amount with 2.8% interest rate.
    Let (31,000-X) be the loan wity 4.5%.
    So put these together equation will come out like this
    ( X * 2.8% ) + ( 31000-X) * 4.5% = 1024.4
    X= 21800 which is the loan amount with 2.8% int rate.
    31000-21800 = 9200 will be the loan amount wity 4.5%.
    you can back test with answer as follow
    21800 @ 2.8% = 610.40
    9200 @ 4.5@ = 414
    610.40 + 414 = 1024.4 so answer is correct
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  3. #3
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    Hello, picturelady!

    Cole's two student loans totaled $31,000.
    One of his loans was at 2.8% simple interest and the other at 4.5%.
    After one year, Cole owed $1024.40 in interest.
    What was the amount of each loan?

    Let x = amount at 2.8%
    . . This cost him: . 0.028x dollars in interest.

    Then the rest, 31,\!000-x = amount at 4.5%
    . . This cost him: . 0.045(31,\!000-x) dollars in interest.

    His total interest charge was: . 0.028x + 0.045(31,\!000-x) dollars.


    But we are told that his total interest charge was: $1024.40.


    There is our equation! . . . . . {\color{blue}0.028x + 0.045(31,\!000-x) \;=\;1024.40}

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