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quantitative problems

Discussion in 'Pre-Dental' started by ibo man, Sep 3, 2002.

  1. ibo man

    ibo man Senior Member

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    Could someone please help me out with these problems.

    A). What is the probability of six tails out of nine tosses of a fair coin? The answer is 21/128. Please explain.

    B). A donut shop bakes a dozen donuts at a cost of $4. To achieve a 33% profit on sales, what is the minimum sale price the donut shop should set each donut? The answer is 50 cents.

    C). A candy store mixes jaw breakers worth 36 cents a pound with lolly pops worth 52 cents a pound to make a 200 pound mixture worth 40 cents a pound. How may pounds of lolly pop did the store use? The answer is 50 pounds.

    I would appreciate it if you could explain the answers to me. Thanks.
     
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  3. portlander

    portlander Member

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    For the 6 tosses out of 9 question:

    This one involves a permutation. What you do is use the formula "n things taken p at a time"

    n!/p! (n-p)!

    Use this equation where 9 is n and 6 is p:

    You get: 9!/6!(9-6)! = 9!/6!(3)! = (9x8x7)/(3x2x1) (cancel out the 6 factorial by extending the 9 factorial)

    This equals 84. This number is the number of possible ways this event can happen.

    THEN, you use the formula 1/2 x 1/2 x 1/2 etc... to calculate the denominator....this number is equal to the number of possible outcomes of each toss.

    So then you have 84/512 wish amazingly reduces to 21/128.

    The easier way to reduce this, which is hard to show on the computer is to write out in the denominator "2x2x2x2x2x2x2x2x2"
    and cancel the factors of 2 in the nominator.

    Did this make any sense? Memorize the permutation equation. It works for figuring out how many ways you can organize X number of people in a line, etc...
     
  4. UBTom

    UBTom Class '04 official geezer

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    Question B is easy too.

    33% is roughly 1/3. So the question is what sum do you sell 12 donuts for in order to keep 1/3 of the sale money as profit?

    So if you sell the 12 donuts for $6, you keep $2 (which is 1/3, or 33.3333333% of $6) as profit after taking away $4 for the cost of making them. And $6 divided by 12 is 50 cents per donut.

    [Homer] Mmmm.... Donut.... [/Homer] Heh heh.. :D

    HTH!
     
  5. mzalendo

    mzalendo Member

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    let the no of jaw breakers be X and the No of lol be y

    x+Y=200
    (.36x+.52y)/(x+Y)=40
    (.36x+.52y)/200=40
    .36x+.52y=.4(200)
    .36x+(200-x).52=80
    .36x+104-.52x=80
    .16x=24
    x=150
    Given that x+y=200
    y=50 answer(No of Lollipops) I hope these are blue coz my favorite color is blue.
     
  6. ibo man

    ibo man Senior Member

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    portlander, UBTom, mzalendo,
    Thank you guys very much. You guys are the greatest. I know I can count on you people. Thanks
     
  7. mzalendo

    mzalendo Member

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    mzalendo has one more thing to say about question 2
    the answer to this problem actually depend on the choices provided. Provided it is a number above 44.33 cents ~.45 centsthis is why
    12 donuts =400 cents
    1 donut =1/12*400cents
    =33.33 cents or like portlander suggested
    33(1/3)cents
    100%=100/3
    133%=(133/100)(100/3)
    =133/3
    =44(1/3)
    confirmation pick any number above 44.33 say 45 cents 12 donuts will cost 5.4 dollars the percentage profit is
    140/400x100=35 %
    any number in the choices above 44.33 even 44.35 cents should work.
    I hope these are choclate glazed donuts coz I love them
     

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