How to Find X, knowing the % of a Number?

[TheCosmicBird]

This math question is stumping me, too:

Tom wants to know which organization (A,B,C,or D) has the largest number of female staff. He knows the number of male staff, and the percentage of female staff for each organization as follows:

A - 289 Male, 49.0300% Female
B - 294 Male, 48.4211% Female
C - 300 Male, 47.6440% Female
D - 302 Male, 46.4539% Female

Using the above, which organization has the largest number of female?

So, I know that the setup is something like "X divided by 289+X" = 49.0300%. (For A). But I'm not clear on how to go about solving for X here.

But yes, any guidance anyone could provide would be sincerely appreciated.

Thank you!
~Cosmic

 

[Deleted member 4993]

This math question is stumping me, too:

Tom wants to know which organization (A,B,C,or D) has the largest number of female staff. He knows the number of male staff, and the percentage of female staff for each organization as follows:

A - 289 Male, 49.0300% Female
B - 294 Male, 48.4211% Female
C - 300 Male, 47.6440% Female
D - 302 Male, 46.4539% Female

Using the above, which organization has the largest number of female?

So, I know that the setup is something like "X divided by 289+X" = 49.0300%. (For A). But I'm not clear on how to go about solving for X here.

But yes, any guidance anyone could provide would be sincerely appreciated.

Thank you!
~Cosmic

Correct - but first define X

Let X = number of females in org. A

Then X / (X + 289) = 0.4903

X = 0.4903 * ( X + 289)

X = X * 0.4903 + 289 * 0.4903

X - X * 0.4903 = 289 * 0.4903

Continue....

 

[TheCosmicBird]

Thank you Khan!

So I get how you got to here:

X = X * 0.4903 + 289 * 0.4903

But just so I'm clear, (this is where my math knowledge breaks down) in order to get to here:

X - X * 0.4903 = 289 * 0.4903

You have to subtract "X * 0.4903" on both sides?

So, X = (X * 0.4903) + (289 * 0.4903)
Then, (X) - (X*0.4903) = (X * 0.4903) - (X * 0.4903) + (289 * 0.4903)
Equals X - X * .4903 = 289 * 0.4903

Then (if I thought about the above correctly) I could say:

X - (X *.4903) = 141.6967

Although, again here the specifics of how to approach the math breaks down for me. I'm not quite sure how to go about solving for X here. Maybe something like:

Subtract X on both sides, so you get:

.4903X = 141.6967 - X. Then you get:

.4903 = (141.6967 -X ) divided by X. Which equals:

.4903 = 141.6967/X, Then multiply X on both sides to get:

.4903X = 141.6967, Then you get:

X = 141.6967/.4903
X = 289

Although, that can't be right haha...since 289 is the number of males in organization A!

Oh boy, I'm definitely not thinking about this correctly somewhere.

Well, I sincerely appreciate any additional guidance you can give. Thank you!
~Cosmic

 

[Dr.Peterson]

This math question is stumping me, too:

Tom wants to know which organization (A,B,C,or D) has the largest number of female staff. He knows the number of male staff, and the percentage of female staff for each organization as follows:

A - 289 Male, 49.0300% Female
B - 294 Male, 48.4211% Female
C - 300 Male, 47.6440% Female
D - 302 Male, 46.4539% Female

Using the above, which organization has the largest number of female?

So, I know that the setup is something like "X divided by 289+X" = 49.0300%. (For A). But I'm not clear on how to go about solving for X here.

But yes, any guidance anyone could provide would be sincerely appreciated.

Thank you!
~Cosmic

You can also do this without algebra.

If 49.0300% are female, what percentage are male?

If that percentage of the whole is 289, what is the whole?

Then how many females are there?

(On the other hand, since you have to do this four times, I might want to make a formula, by using the algebraic method with several variables.)

 

[Deleted member 4993]

Correct - but first define X

Let X = number of females in org. A

Then X / (X + 289) = 0.4903

X = 0.4903 * ( X + 289)

X = X * 0.4903 + 289 * 0.4903

X - X * 0.4903 = 289 * 0.4903

Continue....

X - X * 0.4903 = 289 * 0.4903 ..................... factorize 'X' on the left-hand-side

X * (1 - 0.4903) = 289 * 0.4903

X * 0.5097 = 289 * 0.4903 ...........................divide both sides by 0.5097

X = 289 * 0.4903/0.5097 = 278.0001962 = ~278

Check your answer:

% of male = 289/(289 + 278) =0.509700176

% of female = 278/(289 + 278) =0.490299824 = 0.4903 = 49.03% .......................... checks with given value

 

[TheCosmicBird]

Thank you Khan. This makes sense, although, when you say, "factorize 'X' on the left-hand-side":

X - X * 0.4903 = 289 * 0.4903 ..................... factorize 'X' on the left-hand-side

I'm not clear on how you got:

X * (1 - 0.4903) = 289 * 0.4903

I'm not familiar with the logic on how to factorize X. Is there a particular term I can google to learn this?

Thank you again!

 

[TheCosmicBird]

You can also do this without algebra.

If 49.0300% are female, what percentage are male?

If that percentage of the whole is 289, what is the whole?

Then how many females are there?

(On the other hand, since you have to do this four times, I might want to make a formula, by using the algebraic method with several variables.)

Ah this makes sense. Being that it's clear my algebra logic is quite flawed (I plan on taking an algebra course on Udemy to fix this), this approach works great! The answer is 278 female using this approach, which matches Khan's answer using algebra. Ok, really appreciate this, thank you!