Question

Question #b07ae

Answer 1

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 " " " "color(purple)((1))`

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 * 100/100)^(color(blue)("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 * 100/100)^(color(blue)("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

`111/100m + 120/100f = 6330" " " " color(purple)((2))`

Use equation `color(purple)((1))` to get

`m = 5500 - f`

and plug this into equation `color(purple)((2))`

`111/100 * (5500 - f) + 120/100f = 6330`

Solve this equation for `f`

`610500 - 111f + 120f = 633000`

`9f = 633000 - 610500`

`f = 22500/9 = 2500`

This will get you

`m = 5500 - 2500 = 3000`

So, the initial numbers of males and females were

`{(m = 3000), (f = 2500) :}`

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

`111/100 * 3000 = color(green)("3330 males")`

and

`120/100 * 2500 = color(green)("3000 females")`