# Question b07ae

Oct 16, 2015

Here's what I got.

#### Explanation:

Let's say that the initial number of males is $m$ and the initial number of females is $f$.

At first, the population of the village is $5500$. This means that you can write

$m + f = 5500 \text{ " " } \textcolor{p u r p \le}{\left(1\right)}$

Next, you know that the number of males increases by 11%. You can say that the new number of males will be equal to

${\overbrace{m \cdot \frac{100}{100}}}^{\textcolor{b l u e}{\text{initial no.")) + m * 11/100 = overbrace((100 + 11)/100 * m)^(color(red)("final. no.}}}$

Likewise, the number of females increases by 20%#. The new number of females will be equal to

${\overbrace{f \cdot \frac{100}{100}}}^{\textcolor{b l u e}{\text{initial no.")) + f * 20/100 = overbrace((100 + 20)/100 * f)^(color(red)("final. no.}}}$

The new population of the village is $6330$, which means that a second equation will be

$\frac{111}{100} m + \frac{120}{100} f = 6330 \text{ " " } \textcolor{p u r p \le}{\left(2\right)}$

Use equation $\textcolor{p u r p \le}{\left(1\right)}$ to get

$m = 5500 - f$

and plug this into equation $\textcolor{p u r p \le}{\left(2\right)}$

$\frac{111}{100} \cdot \left(5500 - f\right) + \frac{120}{100} f = 6330$

Solve this equation for $f$

$610500 - 111 f + 120 f = 633000$

$9 f = 633000 - 610500$

$f = \frac{22500}{9} = 2500$

This will get you

$m = 5500 - 2500 = 3000$

So, the initial numbers of males and females were

$\left\{\begin{matrix}m = 3000 \\ f = 2500\end{matrix}\right.$

After the increase in population, the new numbers of males and females will be

$\frac{111}{100} \cdot 3000 = \textcolor{g r e e n}{\text{3330 males}}$

and

$\frac{120}{100} \cdot 2500 = \textcolor{g r e e n}{\text{3000 females}}$