Question

A school district held a meeting for all its physical education teachers.The number of women attending was 5 more than twice the number of men attending. A total of 53 teachers attended the meeting. Which system of equations could be used to find the number of men attending the meeting? How many men attended the meeting?

Answer 1

Answer:

The system of equation is $w+m=53$ and $w=2m+5$.

There are 16 men who are attended the meeting.

Step-by-step explanation:

Given,

Total number of teachers = 53

Solution,

Let the total number of women teachers be 'w'.

And also let the total number of men teachers be 'm'.

So, total number of teachers is the sum of total number of women teachers and total number of men teachers.

This can be framed in equation form as;

$w+m=53\ \ \ \ equation\ 1$

The system of equation is $w+m=53$.

Now according to question,

The number of women attending was 5 more than twice the number of men attending the meeting.

So this can be framed in equation form as;

$w=2m+5\ \ \ equation\ 2$

Now we insert the value of w from equation 2 in equation 1, we get;

$2m+5+m=53\\\\3m+5=53\\\\3m=53-5=48\\\\m=\frac{48}{3}=16$

Now we solve for 'w';

$w=2m+5=2\times16+5=32+5=37$

Hence there are 16 men who attended the meeting.

And also there are 37 women who attended the meeting.