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

Using the expressions you obtained in part A, write an equations to model the situation-example-1
User Riyadh
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1 Answer

10 votes
10 votes

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.

User Tsvi
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