Question

A dance club holds a maximum of 700 people. The club charges one price for students and a higher price for nonstudents. If the number of students in the club at any time is x and the number of nonstudents is y, shade the region that contains all combinations of students and nonstudents that are in the club at any time.

Answer 1

Answer:

The line is drawn at $x+y\leq 700$ and the corresponding area is shaded.

Step-by-step explanation:

As per the given data

Number of students is x

Number of non students is y

so at any given time the

$x+y\leq 700$

For this inequality, converting the corresponding equation and finding the x and y intercepts as below

equation: $x+y= 700$

x intercept: Put x =0 so

                        $x+y= 700\\0+y_1=700\\y_1=700\\P1(0,700)$

So x intercept is (0,700)

y intercept: Put y=0

$x+y= 700\\x_1+o=700\\x_1=700\\P2(700,0)$

So y intercept is (700,0)

Now graphing the equation as indicated in the attachment.

Now as the number of students and non students can not be zero so considering 1st quadrant only and shading the region as below

Put (x,y)=(0,0) in the inequality and check whether it holds or not

$0+0\leq 700\\0\leq 700$

So it holds. Shading the region inclusive of origin as indicated in the attached graph