Question

Using the expressions you obtained in part A, write an equations to model the situation in terms of the variable x.

Answer 1

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

`W=5+3x.........\mleft(1\mright)`

And also, M=4W-3

That is,

`M=4\mleft(5+3x\mright)-3\ldots\ldots\ldots\ldots(2)`

So, the total number of people in terms of x is,

`\begin{gathered} M+W+C=2838 \\ \lbrack4(5+3x)-3\rbrack+\lbrack5+3x\rbrack+x=2838\ldots\ldots\ldots(3) \end{gathered}`

Solving for x, we get

`\begin{gathered} 20+12x-3+5+3x+x=2838 \\ 16x+22=2838 \\ 16x=2816 \\ x=176 \end{gathered}`

Therefore, the number of children is, x=176.

The number of women is,

`5+3(176)=533`

Therefore, the number of women is 533.

The number of men is,

`4(5+3(176))-3=2129`

Therefore, the number of men is 2129.