Question #b07ae

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")#