Chapter 6.5, Problem 34PFA

a.

To determine

To write the system of equations representing the situation

Answer to Problem 34PFA

  $\begin{array}{l}m+w=114\\ m=2w\end{array}$

Explanation of Solution

Given:

Number of people who attended the seminar: 114

There were twice as many women as men at the seminar.

Calculation:

Let m denote the number of men and w denote the number of women.

Total number of people who attended the seminar included men and women

  $\Rightarrow m+w=114$

Also given that there were as many women as men at the seminar.

  $\Rightarrow m=2w$

Conclusion:

The system of equations is $m+w=114$ and $m=2w$

b.

To determine

To find which equation represents the substitution method

Answer to Problem 34PFA

  $w+2w=114$

Explanation of Solution

Given:

From subpart (a),

The system of equations is $m+w=114$ and $m=2w.$

Calculation:

Let,

  $\begin{array}{l}m+w=\mathrm{114..........}(1)\\ m=2w\mathrm{.................}(2)\end{array}$

Substitute (2) in (1)

  $\Rightarrow w+2w=114$

Conclusion:

Therefore, the correct option is $w+2w=114.$

c.

To determine

To solve the system of equations

Answer to Problem 34PFA

Men: 76

Women: 38

Explanation of Solution

Given:

From subpart (a),

The system of equations is,

  $\begin{array}{l}m+w=114\\ m=2w\end{array}$

Calculation:

From subpart (b),

  $\begin{array}{l}\Rightarrow w+2w=114\\ \Rightarrow 3w=114\\ \Rightarrow w=38\end{array}$

Substitute the value of w in $m+w=114,$

  $\begin{array}{l}\Rightarrow m+38=114\\ \Rightarrow m=114-38\\ \Rightarrow m=76\end{array}$

Conclusion:

Therefore, there were 76 men and 38 women who attended the seminar.