Given:
The total number of people is 2838.
The number of women is 5 more than 3 times the number of children.
The number of men is 3 less than 4 times the number of women.
To model this situation in terms of x:
Let x be the number of children.
So, we have
[tex]W=5+3x.........\mleft(1\mright)[/tex]
And also, M=4W-3
That is,
[tex]M=4\mleft(5+3x\mright)-3\ldots\ldots\ldots\ldots(2)[/tex]
So, the total number of people in terms of x is,
[tex]\begin{gathered} M+W+C=2838 \\ \lbrack4(5+3x)-3\rbrack+\lbrack5+3x\rbrack+x=2838\ldots\ldots\ldots(3) \end{gathered}[/tex]
Solving for x, we get
[tex]\begin{gathered} 20+12x-3+5+3x+x=2838 \\ 16x+22=2838 \\ 16x=2816 \\ x=176 \end{gathered}[/tex]
Therefore, the number of children is, x=176.
The number of women is,
[tex]5+3(176)=533[/tex]
Therefore, the number of women is 533.
The number of men is,
[tex]4(5+3(176))-3=2129[/tex]
Therefore, the number of men is 2129.
