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In a corporation, 50 percent of the male employees and 40

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In a corporation, 50 percent of the male employees and 40 [#permalink]

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In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

A. 3/5
B. 2/3
C. 3/4
D. 4/5
E. 5/6
[Reveal] Spoiler: OA
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Re: Percent Problem [#permalink]

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udaymathapati wrote:
In a corporation, 50 percent of the male employees and 40 percent of the female
employees are at least 35 years old. If 42 percent of all the employees are at least 35
years old, what fraction of the employees in the corporation are females?
A. 3/5
B. 2/3
C. 3/4
D. 4/5
E. 5/6


Given weighted average employees who are at least 35 years old: \(\frac{0.5m+0.4f}{m+f}=0.42\). Question: \(\frac{f}{m+f}=?\)

\(\frac{0.5m+0.4f}{m+f}=0.42\) --> \(50m+40f=42m+42f\) --> \(4m=f\) --> \(\frac{f}{m}=4\) --> \(\frac{f}{m+f}=\frac{4}{5}\).

Answer: D.
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Re: Percent Problem [#permalink]

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New post 26 Aug 2010, 08:46
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I have a different approach that may be useful for you:

Let's say that “x” is the % of male employees in the corporation. So, (1-x) is the % of female employees in the same company.
Therefore:
\((50%)(x) + (40%)(1-x) = 42%\)

Expressed in fractions:
\((1/2)(x) + (2/5)(1-x) = 21/50\)

We solve the equation and we have:
\(x = 1/5\)

\((1-x) = 4/5\)

Answer: 4/5 : D

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Re: Percent Problem [#permalink]

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Hi Buneul -

I understood your explanation until the last step. How do you get from f/m= 4 to the 4/5?

Thanks!
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Re: Percent Problem [#permalink]

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Re: GWD #1 Math 11 [#permalink]

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eybrj2 wrote:
In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?

a) 3/5

b) 2/3

c) 3/4

d) 4/5

e) 5/6


You can use the weighted averages formula for a 10 sec solution.

No of females/No of males = (50 - 42)/(42 - 40 ) = 4/1

No of females as a fraction of total employees = 4/(4+1) = 4/5

For details of this method, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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Let Male employees = x

Let Female employees = y

Total Employees = x+y

We require to find \(\frac{y}{x+y}\)

Setting up the equation:

\(\frac{50x}{100} + \frac{40y}{100} = \frac{42}{100} (x+y)\)

\(\frac{y}{x} = 4\)

\(\frac{y}{x+y} = \frac{4}{1+4} = \frac{4}{5}\)

Answer = E
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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x- total number of employees
f - all females
x-f - all males

we need f/x

50(x-f)+40f=42x
50x-50f+40f=42x
10f=8x
f/x=8/10=4/5

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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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New post 22 Aug 2016, 06:08
.5m+.40f=.42
m+f=1

solve these two equations,
f=4/5
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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New post 06 Nov 2016, 19:47
I used the 2 way chart to help create the expression :

(50/100)x + (40/100)y = 42/100(x+y) .... where x is number of males, y is number of females and x+y is total.

Now when you simplify it, you will get 4x = y. Means for every 4 females there is 1 male... No of females is 80% or 4/5
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Re: In a corporation, 50 percent of the male employees and 40 [#permalink]

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New post 16 Dec 2017, 08:32
Males + Females =100 - Equation 1

50 * Males + 40 * Females = 42 [ Males + Females ] - Equation 2

Solve for Females.

You will get 80 Answer ( Which is 80%)

therefore = 80/100=4/5
Re: In a corporation, 50 percent of the male employees and 40   [#permalink] 16 Dec 2017, 08:32
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