Results 1 to 3 of 3

Thread: mixture question

  1. #1
    Senior Member euclid2's Avatar
    Joined
    May 2008
    From
    Ottawa, Canada
    Posts
    400
    Awards
    1

    mixture question

    Conrad works at a bulk-food store. His manager asks him to mix some
    dried fruit (that cost $3.75/kg) with some granola (that costs $1.75/kg) to
    make 30 kg of trail mix that will sell for $2.75/kg. How many kilograms of
    dried fruit are in the trail mix?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2008
    Posts
    792
    I drew this table to make things clearer for you.


    The total price is found by multiplying the Price/Weight by Weight. Now, let's analyze the table. We can see that the total price is expressed as:

    $\displaystyle a + b = 82.5$

    But we still need another relation. Let's go back to the table. We can see that the total weight is expressed as:

    $\displaystyle c + d = 30$

    But what is c and d?

    Remember, they gave you the price/weight for dried fruits:
    $\displaystyle \frac{a}{c} = 3.75$

    $\displaystyle \frac{b}{d} = 1.75$

    Can you work your way from here?

    Hint:
    Try to write the total weight expression in terms of a and b. Then it only becomes a matter of simple substitution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, euclid2!

    Conrad works at a bulk-food store.
    His manager asks him to mix some dried fruit that cost $3.75/kg
    with some granola that costs $1.75/kg
    to make 30 kg of trail mix that will sell for $2.75/kg.
    How many kilograms of dried fruit are in the trail mix?

    Let $\displaystyle x$ = number of kilograms of fruit.
    . . At $3.75/kg, its total value is: .$\displaystyle 3.75x$ dollars.
    Write that into the first row of our chart.

    $\displaystyle \begin{array}{c|c|c|c|}
    & & \text{Unit} & \text{Total} \\
    & \text{kg.} & \text{price} & \text{value} \\ \hline
    \text{Fruit} & x & \$3.75 & 3.75x \\
    \text{Granola} & & & \\ \hline
    \text{Mixture} & & & \end{array}$



    Then $\displaystyle (30-x)$ = number of kilograms of granola.
    . . At $1.75/kg, its total value is: .$\displaystyle 1.75(30-x)$ dollars.
    Write that in the second row of our chart.

    $\displaystyle \begin{array}{c|c|c|c|}
    & & \text{Unit} & \text{Total} \\
    & \text{kg.} & \text{price} & \text{value} \\ \hline
    \text{Fruit} & x & \$3.75 & 3.75x \\
    \text{Granola} & 30-x & \$1.75 & 1.75(30-x) \\ \hline
    \text{Mixture} & & & \end{array}$



    The final mixture is 30 kg of mix worth $2.75/kg.
    . . Its total value is: .$\displaystyle (30)(\$2.75) \:=\:\$82.50$
    Write that in the third row of our chart.

    $\displaystyle \begin{array}{c|c|c|c|}
    & & \text{Unit} & \text{Total} \\
    & \text{kg.} & \text{price} & \text{value} \\ \hline
    \text{Fruit} & x & \$3.75 & 3.75x \\
    \text{Granola} & 30-x & \$1.75 & 1.75(30-x) \\ \hline
    \text{Mixture} & 30 & \$2.75 & 82.50 \end{array}$



    The third column gives us our equation:

    . . $\displaystyle \text{(Total Value of Fruit) } + \text{ (Total Value of Granola)} \;=\;\text{(Total Value of Mixture)}$


    Therefore, we have: .$\displaystyle {\color{blue}3.75x + 1.75(30-x) \;=\;82.50}$

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mixture
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: Mar 31st 2011, 08:07 AM
  2. Differentiate a mixture of e's
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Dec 7th 2009, 09:12 AM
  3. Acid mixture question
    Posted in the Algebra Forum
    Replies: 6
    Last Post: May 2nd 2009, 04:27 AM
  4. Another mixture one
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Apr 23rd 2008, 01:46 PM
  5. Replies: 3
    Last Post: Jun 11th 2006, 08:08 PM

Search Tags


/mathhelpforum @mathhelpforum