# percents and fractions

• Nov 6th 2008, 01:02 PM
nancymcwilliams
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
• Nov 6th 2008, 10:58 PM
earboth
Quote:

Originally Posted by nancymcwilliams
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 $20\% = \dfrac15$

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

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

$51=\dfrac{17}{60} x~\implies~x=\dfrac{51 \cdot 60}{17}=180\ seats$
• Nov 20th 2008, 01:00 PM
nancymcwilliams
I really do not understand where some of the numbers came from in your answer
• Nov 20th 2008, 02:25 PM
jahichuanna
Quote:

Originally Posted by nancymcwilliams
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.
• Nov 21st 2008, 12:06 AM
earboth
Quote:

Originally Posted by nancymcwilliams
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:

$
\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}
$
• Nov 22nd 2008, 08:00 AM
syathish
Quote:

Originally Posted by earboth
Not sure which numbers are not clear to you I'll show you where I've got the numbers from:

$
\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}
$

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!! ;)
• Nov 23rd 2008, 12:11 AM
earboth
Quote:

Originally Posted by syathish
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
• Nov 24th 2008, 01:20 PM
nancymcwilliams
It is the number of seats not passengers but i really appreaciate both answers. together I was able to figure the problem out.
• Dec 3rd 2008, 03:21 AM
repcvt
Quote:

Originally Posted by earboth
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 $\left(\dfrac15 + \dfrac14 + \dfrac18\right)\cdot \dfrac23x+51=\dfrac23 x$