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Math Help - Mixture of Nuts and Investments

  1. #1
    Member Jonboy's Avatar
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    Mixture of Nuts and Investments

    I would like some help on these problems.

    The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound and walnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for $1.75 per pound?

    I came up with the equation:

    23.25 + 1.95x = 1.75 (x + 15)

    And got I got x to be 2.5, so I think I need 2.5 pounds of walnuts.

    And on this problem I'm immensely confounded, A push in the right direction is vitally needed:

    Alice Gleason invested a portion of $32,000 at 9% interest and the balance at 11% interest. How much did she invest at each rate if her total income from both investments are $3,200?
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  2. #2
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    Hello, Jonboy!

    For the first one, your equation is correct.
    Your algebra must have been off . . .


    The Quik Mart has two kinds of nuts.
    Pecans sell for $1.55 per pound and walnuts sell for $1.95 per pound.
    How many pounds of walnuts must be added to 15 pounds of pecans
    to make a mixture that sells for $1.75 per pound?

    I came up with the equation: . 23.25 + 1.95x \:=\: 1.75 (x + 15) . . . . Right!

    And I got x to be 2.5 . . . . no

    You should have: . 23.25 + 1.95x \;=\;1.75x + 26.25

    Then: . 0.2x \:=\:3\quad\Rightarrow\quad \boxed{x \:=\:15}




    Alice Gleason invested a portion of $32,000 at 9% interest and the balance at 11% interest.
    How much did she invest at each rate if her total income from both investments are $3,200?
    This is the easier of the two problems . . .


    Let x = amount invested at 9%.
    . . It earned: . 0.09x dollars.

    Then 32,000-x = amount invested at 11%.
    . . It earned: . 0.11(32,000 - x) dollars.


    The total earnings was $3,200.

    There is our equation! . . . \boxed{\;0.09x + 0.11(32,00 - x) \:=\:3,200\;}

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  3. #3
    Member Jonboy's Avatar
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    hey i'm proud i got the equation correct!
    Lol yeah the second is the easiest.
    Thank you again Soroban!
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  4. #4
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    Investment

    Nuts & Investments

    Investments.

    It seems your figures are wrong somewhere. The equation is this, but, yes, there is a but:

    Say you invest x at 9%, then you invest (32,000 - x) at 11%.

    The equation is: (9x)/100 + (11/100)*(32000 - x) = 3200

    But, yes that but, this equation gives a negative value of x. This must mean that i) either the figure invested is given wrongly.

    or ii) the figure for the total interest is wrong.

    or iii) the percentage figures are wrong.

    But, yes, one more but, the equation is correct.
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