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: \(\frac{R * (100 + F) }{ 100 + M}\).