Chapter 1.6, Problem 3P

To determine

To translate: Each of the two given problem related to a jury of men and women into an equation and also find the number of men in the jury

Answer to Problem 3P

The number of men in the jury is $8$

Explanation of Solution

Given Information:

The statements

(1) There were 12 people in a jury

(2) The number of men in the jury is 4 more than the number of women

The given statements express the relation between the number of men and women in a jury.

1. The first statement implies the total number of people in a jury which is 12.

2. The second statement implies the relation between the number of men and women .

Now, to convert these statements into suitable equation, one of the count is to be assigned a variable and the other count to be expressed in terms of the first variable.

Let the number of women in the jury be x

(A) Based on the statement in (2), the number of men is x+ 4.

(B) Now, as per statement (1), the equation connecting the number of men and women can be written as,

  $x+\left(x+4\right)=12$

Solving the above equation leads to the number of women in the jury. The solution is,

  $\begin{array}{l}2x+4=12\\ x=4\end{array}$

This gives the number of women as 4. Now, based on the relation in (A), the number of men in the jury is given by,

  $\begin{array}{c}\text{No: of men}=x+4\\ \text{}=4+4\\ =8\end{array}$