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 w, the number of women, and m, the number of men, at this meeting?

Step-by-step explanation:

From the given information:

let the number of women be w;&

the number of men be equal to = m

SO;  if the school district held a meeting for all its physical education teachers, both the number of women and men must be equal to the total number of teachers attending the meeting.

w + m = 53     (1)

However, if the number of women was 5 more than twice the number of men;

Then:

2m + 5 = w     Let that be equation (2)

Then, we can now replace the value of w in equation (2) into equation (1).

w  + m = 53

(2m + 5) + m = 53

3m + 5 = 53

3m = 53 - 5

3m = 48

m = 48/3

m = 16

From equation (1)

w + m = 53

w + 16 = 53

w = 53 -16

w = 37

Therefore, the number of women w = 37 and the number of men = 16

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."