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It can be derived with accuracy the number of male and female statistically from the information provided.

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male voters(in the year 2000)= 3300..............(A)

F=100x [Female voters(2020)-Female voters(2000)]/Female voters(2000)..............(B)
M= 100x [Male voters(2020)-Male voters(2000)]/Male voters(2000)..............(C)

R= Female voters(2000)/Male voters(2000) ..............(D)

(i) No of Female voters(2000)
from (A) & (D): Female voters(2000) =R x 3300

(ii) Ratio of female to male voters in the year 2020
­From (B): Female voters(2020)= (F/100) x Female voters(2000)+Female voters(2000)
Female voters(2020)= Female voters(2000)x [(F+100)/100] ..............(E)

Similarly from (C), we get:
Male voters(2020)= Male voters(2000)x [(M+100)/100] ..............(F)

Required Ratio=(E)/(F)=[Female voters(2000)/Male voters(2000)]x [(F+100)/(M+100)]

­Required Ratio=Rx [(F+100)/(M+100)]
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Bunuel
In the town of Xionia, elections were held every 5 years, between the year 2000 to the year 2020. During the 5 elections held in this period, the number of female voters increased while the number of male voters decreased from 3300 in the year 2000.

In the given expressions, F and M represent the percentage change in the number of female and male voters, respectively, over the 5 elections, and R represents the ratio of female to male voters in the year 2000. The percentage change in voters is calculated as \(\frac{\text{number of new voters – number of old voters}}{\text{number of old voters}}* 100\).

Select the expression that represents the Number of female voters in the year 2000, and select the expression that represents the Ratio of female to male voters in the year 2020. Make only two selections, one in each column.
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  • Initial Ratio in 2000: In the year 2000, the ratio of female to male voters is R
  • Changes Over 5 Elections:


    • The number of female voters increases by F%
    • The number of male voters decreases by M%
Ratio in 2020=Number of male voters in 2020/Number of female voters in 2020​

Number of female voters in 2020 = Initial number of female voters×(1+F/100)

Number of male voters in 2020 = Initial number of male voters×(1−M/100)Ratio in 2020=
InitialFemale×(1+F/100​) / InitialMale×(1-M/100​)​

InitialFemale / InitialMale = R

R(2020) = R*(F+100/100-M)
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­Let no. of female voters in 2000 = f and no. of male voters in 2000 = m
Given R=f/m and m=3300.
Therefore, f=R*m=3300R.

For part I, Number of female voters in the year 2000 = 3300R.

Now for part II, Ratio of female to male voters in the year 2020:

We know F, M = % change in female and male voters, respectively over 5 years.

­Let no. of female voters in 2020 = f' and no. of male voters in 2020 = m'

Therefore F = \(\frac{f'-f}{f}\)*100% =\((\frac{ f'}{f}-1)\)*100%

and M = \(\frac{m'-m}{m}\)*100% =\((\frac{ m'}{m}-1)\)*100%

Thus we can find f' and m' in terms of F, f and M, m respectively.

Once we have f' and m', we can find the ratio of female to male voters as: \(\frac{f'}{m'}\)

On solving it gives us, \(\frac{f}{m}*\frac{(100+F)}{(100+M)}\), and we know \(\frac{f}{m}\) = R

Therefore the answer is \(R*\frac{(100+F)}{(100+M)}\).

Sorry for the poor formatting.­
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­Since, in 2000 there are 3300 male voters, and R = number of female voters/ number of male voters
number of female voters in 2000 = R*number of male voters = 3300R

Moreover, there is an increase in the number of female voters by F percentage, and decrease in the number of male voters by M percentage, therefore, the ration of female to male voters must have increased, and that is possible if R is multiplied to a greater numerator than the denominator, and accounting the percent changes, the new ratio in 2020 is R* (100+F)/(100-M)
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­Number of Male voters in 2000 = 3300
R represents the ratio of female to male voters in the year 2000
R = number of feale voters in 2000 / 3300
hence, Number of Female voters in 2000 = 3300 * R

Let female voters in 2020 be X and male voters in 2020 be Y

F  = % change (increase) in the number of female voters 
F = \(\frac{(X - 3300R)}{3300R } * 100\)
.
Upon Solving, we get\( X = 3300 R * \frac{(100+F)}{100}\)

Similarly
M  = % change (decrease) in the number of male voters
\(M = \frac{(3300 - Y)}{3300} * 100\)
.
Upon Solving, we get \(Y = \frac{(100-M)}{100}\).

Hence Ratio of female to male voters in the year 2020 = X/Y
both 3300 gets cancelled out 
= \(\frac{( \frac{R * (100+F)}{100})}{( \frac{(100-M)}{100})}\)­

= \(\frac{R * (100+F)}{(100-M)}\)­
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We'll start by expressing the given values with more detail:

\(F\) and \( M\) stand for the overall change over 5 elections, meaning they are comparing \(f_1\) and \(f_5\), as well as \(m_1\) and \(m_5\) (where \(f\) and \(m\) stand for the number of women and men, respectively, in the first and the last election). Also, we know that \(m_1 = 3300.\)

Therefore, inputting this in the formula for percentage change gives:

\(F = \frac{f_5 - f_1 }{ f_1} * 100\)

\(M = \frac{m_5 - m_1 }{ m_1} * 100 = \frac{m_5 - 3300 }{ 3300 } * 100\)­

Also, R is the ration of women to men in 2000, or in other words, at the first election:

\(R =\frac{ f_1 }{ m_1} =\frac{ f_1 }{ 3300}\)

Effectively, this already gives us the answer to the first question, which asks for \(f_1\):
\(f_1 = 3300R\)

Now with the second question it's a little more difficult but still doable. Let's write out the ratio in the last election year and try to define it differently:
\(R_5 =\frac{ f_5 }{ m_5}\)
We can get \(m_5\) from \(M\):

\(m_5 - 3300= 3300M\)
\(m_5 = 3300M + 3300 = 3300 (M + 1)\)

And we can obtain \(f_5\) from \(F \)as well:

\(f_5 - f_1 = F * f_1 = F * 3300R\)
\(f_5 = F*3300R + f_1 = F*3300R + 3300R = 3300R (F + 1)\)
­
Therefore, \(R_5=\frac{ 3300R (F + 1)}{ 3300 (M + 1)} = \frac{ R(F+1) }{ M+1 }\)
Inputting 100% instead of 1, we easily get the third answer: \(\frac{R * (100 + F) }{ 100 + M}\).­
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Let the number of female voters in 2020 and in 2000 respectively be \(f_{2020}\) and \(f_{2020}\). Same for male \(m_{2020}\) and \(m_{2020}\).
We know that \(m_{2020}=3300\), and R represents the ratio of female to male voters in the year 2000 so 

\(R=\frac{ f_{2000}}{m_{2000}} =>  f_{2000}=m_{2000}*R = 3300*R \) 

So the first answer is  3300*R

As explained in the stem the percentage change in the number of female voters is: 

\(F=\frac{f_{2020} - f_{2000}}{f_{2000}} * 100\)

Therefore the number of female voters in 2020 is:

\(f_{2020} = F * \frac{1}{100} *f_{2000} + f_{2000} = f_{2000} * ( 1 + F * \frac{1}{100}) ­\)­

Same for male 

\(m_{2020} = m_{2000} * ( 1 + M * \frac{1}{100}) ­\)­

Then the ratio of female voters to male voters in 2020 is:

\(\frac{f_{2020}}{m_{2020}} = \frac{ f_{2000}}{m_{2000}} * \frac{1 + F * \frac{1}{100}}{1 + M * \frac{1}{100}} = R *  \frac{100 + F}{100 + M} \)­

The second answer is  \( R *  \frac{100 + F}{100 + M} \)­

 ­
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­Answer:
Number of female voters in the year 2000 : 3300R
Ratio of female to male voters in the year 2020: R∗((100+F)/(100+M))
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Bunuel
In the town of Xionia, elections were held every 5 years, between the year 2000 to the year 2020. During the 5 elections held in this period, the number of female voters increased while the number of male voters decreased from 3300 in the year 2000.

In the given expressions, F and M represent the percentage change in the number of female and male voters, respectively, over the 5 elections, and R represents the ratio of female to male voters in the year 2000. The percentage change in voters is calculated as \(\frac{\text{number of new voters – number of old voters}}{\text{number of old voters}}* 100\).

Select the expression that represents the Number of female voters in the year 2000, and select the expression that represents the Ratio of female to male voters in the year 2020. Make only two selections, one in each column.
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  In 2000, the number of males was 3300, if R were the ratio of Females to Males, say R= a:b where a and b are co-prime, then for some positive integer k, bk=3300 and ak is the number of females; this gives us k=3300/b and hence,
number of females= ak= a*(3300/b) or 3300*(a/b) or 3300R.

In 2020 the number of Females increases by F percent and that of Males increases by M percent. Giving the new numbers as following:
Females= 3300R*(1+[F][/100]) and Males= 3300*(1+[M][/100])
Solving which gives us the ratio of Females to Males in 2020 as R*[100+F][/100+M]
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The first one is straight forward : We know that the number of male voters in year 2000 is 3300, and R represents the ratio of female to male voters in the year 2000 so the number of female voters in year 2000 is simply the product of both => the correct answer is 3300*R

The second one needs more computaion :
In the question stem F is defined as the percentage change in the number of female :
\(F=\frac{nf_{2020} - nf_{2000}}{nf_{2000}} * 100\)
Consequently, the number of female voters in 2020 is :
\(nf_{2020} = \frac{F}{100} *nf_{2000} + nf_{2000} = nf_{2000} * ( 1 + \frac{F}{100}) ­\)­    (equation 1) 
In the same manner, the number of male voters in 2020 is :
\(nm_{2020} = nm_{2000} * (1 + \frac{M}{100}) ­\)­        (equation 2) 

By dividing equation (1) on (2) the ratio of female voters to male voters in 2020 is:
\(\frac{nf_{2020}}{nm_{2020}} = R *  \frac{100 + F}{100 + M} \)­
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Bunuel
In the town of Xionia, elections were held every 5 years, between the year 2000 to the year 2020. During the 5 elections held in this period, the number of female voters increased while the number of male voters decreased from 3300 in the year 2000.

In the given expressions, F and M represent the percentage change in the number of female and male voters, respectively, over the 5 elections, and R represents the ratio of female to male voters in the year 2000. The percentage change in voters is calculated as \(\frac{\text{number of new voters – number of old voters}}{\text{number of old voters}}* 100\).

Select the expression that represents the Number of female voters in the year 2000, and select the expression that represents the Ratio of female to male voters in the year 2020. Make only two selections, one in each column.
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­ Male voters in Year 2000= 3300 , it decreased 
Female voters = unknown , but it increased
F = % change in Female voters
M = % change in Male voters
R = Female /Male voter ratio in 2000
Hence Female voters in Year 2000 = 3300R

M = (1 - new male voters in year 2020/3300 )*100
new male voters in Year 2020 =  (1 - M/100)*3300

F = (new female voters in year 2020/3300R -1)*100
new female voters in Year 2020 = (1+ F/100)*3300R

Female to Male voters in 2020 = (1 +F/100)*3300R/ [(1-M/100)*3300]
= (100+F)*R /(100-M)




 
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number of females 2000=x
number of males 2000=y=3300

R=x/y
R=x/3300

Number of female 2000= x=3300R
number of females 2020=w
number of males 2020=z
F=(( w-x)/x)*100
M=(( z-y)/x)*100
x=3300R
y=3300
Ratio2020= x(1+(F/100)/y(1-(M/100))

Ratio2020=3300R(1+(F/100))/3300(1-(M/100))

Ratio2020=R*(1+(F/100))/(1-(M/100))

Ratio2020=R*((100+F)/100)/((100-M)/100)

Ratio2020=R*((100+F)/((100-M)
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­R = # of Female voters / # of Male voters in 2000

1) # of Female voters = R * # of Male voters
(Given that # of Male voters in 2000 = 3300)
Therefore, # of Female voters = 3300R

2) New Ratio: Given that # of Female voters increased and # of Male voters decreased
Therefore new ration = R * 100+F/100-M
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Bunuel
In the town of Xionia, elections were held every 5 years, between the year 2000 to the year 2020. During the 5 elections held in this period, the number of female voters increased while the number of male voters decreased from 3300 in the year 2000.

In the given expressions, F and M represent the percentage change in the number of female and male voters, respectively, over the 5 elections, and R represents the ratio of female to male voters in the year 2000. The percentage change in voters is calculated as \(\frac{\text{number of new voters – number of old voters}}{\text{number of old voters}}* 100\).

Select the expression that represents the Number of female voters in the year 2000, and select the expression that represents the Ratio of female to male voters in the year 2020. Make only two selections, one in each column.
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­Let's draw the timeline with the given information,

2000-------------'05---------------'10-------------'15--------------2020
Male: 3300                                                                    Percent change F and M in female and male population from the year 2000
Female: ?
R=Female/Male

Column 1: Female pop in 2000 is simple to calculate: R = female/male, we know male pop = 3300 in the year 2000
So, female pop =
\(3300*R \)- ANSWER 1

Column 2: Ratio of female pop to male pop in 2020 is: female pop in 2020/male pop in 2020, by finding these two values we can get the ratio.

Female pop in 2020 = female pop in 2000 (1+F/100) =>
\(3300*R*(100 +F)/100\)

Male pop in 2020 = male pop in 2000 (1+M/100) =>\( 3300*(100+M)/100\)

Putting these back in the ratio equation, \(\frac{\text{3300*R*(100+F)/100}}{\text{3300*(100+M)/100}}\)

We get, ­\(\frac{\text{R*(100+F)}}{\text{(100+M)}}\)­ ANSWER 2
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­Please find attached the explanation. ­
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Let's write down what's given :
Males in (2000) - 3300
Males in (2020) - x
Females in (2000) - y
Females in (2020) - y'

F = (y'-y) / y *100 ----(1)
M = (x-3300) / 3300 *100 -----(2)
R = y / 3300
y = 3300R - No of females in 2000


Solving for (1) and (2),
y' = (F/100 + 1) * y
x = (M/100 + 1) * 3300
We need y' / x
Dividing , we get
(F+100)*y / (M+100)*3300
Plugging value of Y = 3300R
(F+100)*3300R / (M+100)*3300
R*(F+1) / (M+100)
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