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Thread: few algabra questions, need help!

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    few algabra questions, need help!

    Need help on a few algabra problems.
    solve the equation for the indicated variable
    1. F=9/5C+32, for C

    2. Kevin invested part of his $10,000 bonus in a certificate of a deposit that paid 6% annual simple intrest, and the remmainder in a mutual fun that paid 11% annual simple interest. if his total interst for that year was $900, how much did Kevin invest in the mutual fund?

    3. Ken and Kara are 29 miles apart on a calm lake paddling towards each other. Ken paddles at 4 miles per hour while Kara paddles at 7 miles per hour. How long will it take them to meet?

    4. A chemist needs 110 mL of a 65% solution but only has 53% and 97% solutions available. Find how many mL of each that should be mixed to get the desired solution.
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    Quote Originally Posted by mathnoobie25 View Post
    solve the equation for the indicated variable
    1. F=9/5C+32, for C
    $\displaystyle F = \frac{9}{5}C + 32$

    $\displaystyle F - 32 = \frac{9}{5}C + 32 - 32$

    $\displaystyle F - 32 = \frac{9}{5}C$

    $\displaystyle \frac{5}{9}(F - 32) = \frac{5}{9} \cdot \frac{9}{5}C$

    $\displaystyle \frac{5}{9}(F - 32) = C$

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mathnoobie25 View Post
    3. Ken and Kara are 29 miles apart on a calm lake paddling towards each other. Ken paddles at 4 miles per hour while Kara paddles at 7 miles per hour. How long will it take them to meet?
    Ken is moving at 4 mi/h and covers a distance of x mi in t hours.
    Kara is moving at 7 mi/h and covers a distance of y mi in t hours. (Obviously they meet at the same time!)
    And we know that, combined, they covered x + y = 29 mi.

    Thus:
    $\displaystyle 4 = \frac{x}{t}$

    So
    $\displaystyle x = 4t$

    and
    $\displaystyle 7 = \frac{y}{t}$

    So
    $\displaystyle y = 7t$

    And
    $\displaystyle x + y = 29$

    $\displaystyle 4t + 7t = 29$

    $\displaystyle 11t = 29$

    $\displaystyle \frac{1}{11} \cdot 11t = \frac{1}{11} \cdot 29$

    $\displaystyle t = \frac{29}{11}$

    So it takes them about 2.64 hrs to meet.

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mathnoobie25 View Post
    4. A chemist needs 110 mL of a 65% solution but only has 53% and 97% solutions available. Find how many mL of each that should be mixed to get the desired solution.
    We want a total volume of 110 mL of solution at the end. This means we need
    $\displaystyle 0.65 \cdot 110 = 71.5$ mg of solute.

    So we are going to mix "x" mL of the 53% solution with "y" mL of the 97% solution to get x + y = 110 mL of final solution.

    We will have $\displaystyle 0.53 \cdot x + 0.97 \cdot y = 71.5$ mg of solute in the final solution.

    So:
    $\displaystyle x + y = 110$
    $\displaystyle 0.53x + 0.97y = 71.5$

    From the first equation:
    $\displaystyle y = 110 - x$

    Inserting this into the second equation gives:
    $\displaystyle 0.53x + 0.97(110 - x) = 71.5$

    $\displaystyle 0.53x + 106.7 - 0.97x = 71.5$

    $\displaystyle -0.44x = -35.2$

    $\displaystyle x = 80$

    Thus we need 80 mL of the 53% solution and 110 mL - 80 mL = 30 mL of the 97% solution.

    -Dan
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