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30 September, 00:04

A man invested one fifth of his money at 4%, half of his money at 5%, and the rest of his money at 3.5%. If his total annual investment income was $870, how much had he invested?

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  1. 30 September, 00:19
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    The man invested 1/5 of the money at 4/100. Which says he earns 4/500 of his total money on one month.

    He also invested 1/2 of the money at 5/100. Which means he earns 5/200 of his total money per month.

    For the last part, he spent the rest of the money which is: x + 1/5 + 1/2 = 1

    Make the denominators equal: x + 2/10 + 5/10 = 10/10

    Add like terms: x + 7/10 = 10/10

    Substract 7/10: x=3/10

    He gave this money for 3.5/100 interest. Which equals 10.5/1000 of his total money.

    When you add the three values: 4/500 + 5/200 + 10.5/1000

    Make denominators equal: 8/1000 + 25/1000 + 10.5/1000

    Add the like terms: 43.5/1000

    This means the man's money's 43.5/1000 is equal to $870

    Set the values equal: 43.5x/1000 = 870

    Make the denominators equal: 43.5x/1000 = 870,000/1000

    Multiply with 1000: 43.5x = 870,000

    Divide both sides by 43.5: x = 20,000

    The man's total money is $20,000
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