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Math Help - percents and fractions

  1. #1
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    percents and fractions

    On an airplane that was 2/3 full, 20% of the passengers were boys, one-fourth of the passengers were women, one-eighth of the passengers were girls, and there were 51 men. How many seats are on the plane
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    Quote Originally Posted by nancymcwilliams View Post
    On an airplane that was 2/3 full, 20% of the passengers were boys, one-fourth of the passengers were women, one-eighth of the passengers were girls, and there were 51 men. How many seats are on the plane
    Let x denote the total number of seats in the plane.
    Translate the sentence into numbers and operations. Keep in mind that 20\% = \dfrac15

    \left(\dfrac15 + \dfrac14 + \dfrac18\right)\cdot x+51=\dfrac23 x

     \dfrac{23}{60} \cdot x +51=\dfrac23 \cdot x

    51=\dfrac{17}{60} x~\implies~x=\dfrac{51 \cdot 60}{17}=180\ seats
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  3. #3
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    I really do not understand where some of the numbers came from in your answer
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    Quote Originally Posted by nancymcwilliams View Post
    On an airplane that was 2/3 full, 20% of the passengers were boys, one-fourth of the passengers were women, one-eighth of the passengers were girls, and there were 51 men. How many seats are on the plane
    the first thing you want to do is convert everything to either a fraction/ratio or a number
    so it becomes

    an airplane 2/3 full, 20% passengers were boys, 25% women, 12.5% girls, 51 men.


    now, since you need 100%, you figure out what percent you have now: 20+25+12.5 = 57.5%

    so 57.5% of the passengers WERE NOT men. That means that 42.5% WERE men. Since 42.5% were men, figure out how many passengers there are altogether. A percentage can become a decimal, e.g. 1% = .01; 42.5% = .425. Therefore, 42.5% of x = 51 becomes .425x=51. Solve for x and get 120. That means there were 120 total PASSENGERS on the plane. Since the plane is 2/3 full, do 2/3 y = 120. solve for y and get 180.
    So there are 180 seats on the plane.


    hope this helped you out.
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    Quote Originally Posted by nancymcwilliams View Post
    I really do not understand where some of the numbers came from in your answer
    Not sure which numbers are not clear to you I'll show you where I've got the numbers from:

    <br />
\overbrace{\left(\underbrace{\dfrac15}_{boys} + \underbrace{\dfrac14}_{women} + \underbrace{\dfrac18}_{girls}\right)}^{fractions\ of\ all\ seats}\cdot x+\underbrace{51}_{men}=\underbrace{\dfrac23 x}_{occupied\ seats}<br />
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    Quote Originally Posted by earboth View Post
    Not sure which numbers are not clear to you I'll show you where I've got the numbers from:

    <br />
\overbrace{\left(\underbrace{\dfrac15}_{boys} + \underbrace{\dfrac14}_{women} + \underbrace{\dfrac18}_{girls}\right)}^{fractions\ of\ all\ seats}\cdot x+\underbrace{51}_{men}=\underbrace{\dfrac23 x}_{occupied\ seats}<br />
    i think the question says 20%of the passengers not 20%of the total seats
    The same goes to women and girls in which case supposing x=total seats then
    the no of the passengers is 2x/3 then 20% of the passengers=1/5 of 2x/3
    pardon me if i am wrong though!!
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  7. #7
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    Quote Originally Posted by syathish View Post
    i think the question says 20%of the passengers not 20%of the total seats
    The same goes to women and girls in which case supposing x=total seats then
    the no of the passengers is 2x/3 then 20% of the passengers=1/5 of 2x/3
    pardon me if i am wrong though!!
    You are completely right. (In my first post I made a very advantageous error so I got the correct final result) In short:

    Let t denote the total number of seats and x the number of occupied seats. Then you have a system of simultaneous equations:

    \left|\begin{array}{r}\dfrac23 t = x \\ \dfrac15 x+\dfrac14 x + \dfrac18 x + 51 = x\end{array}\right.

    You'll get x = 120 and t = 180
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  8. #8
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    It is the number of seats not passengers but i really appreaciate both answers. together I was able to figure the problem out.
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  9. #9
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    Quote Originally Posted by earboth View Post
    Let x denote the total number of seats in the plane.
    Translate the sentence into numbers and operations. Keep in mind that 20\% = \dfrac15

    \left(\dfrac15 + \dfrac14 + \dfrac18\right)\cdot x+51=\dfrac23 x

     \dfrac{23}{60} \cdot x +51=\dfrac23 \cdot x

    51=\dfrac{17}{60} x~\implies~x=\dfrac{51 \cdot 60}{17}=180\ seats

    should be \left(\dfrac15 + \dfrac14 + \dfrac18\right)\cdot \dfrac23x+51=\dfrac23 x

    simple answer is 51/(1-1/5-1/4-1/8)*3/2=180
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