Question 944177
Let us define variables:
{{{x}}}= number of adults who purchased tickets
{{{y}}}= number of children who had tickets
So,
{{{250x}}}= amount (in pesos) collected for all the adult tickets sold
{{{200y}}}= amount (in pesos) collected for all the children tickets sold
Since "more than 150 adults and children" watched the plane, "
{{{x+y>150}}}
Since "The sponsor of the show collected a total amount of not more than 44,000 pesos",
{{{250x+200y<=44000}}} .
 
a. The mathematical statement (or statements) the represent the given situation is (or are)
{{{system(x+y>150,250x+200y<=44000)}}} .
 
b. To graph an inequality, such as {{{x+y>150}}} , you draw boundary lines for the region that is the solution, and color or shade the region that is the solution.
You draw a solid line when the points on that line are part of the solution.
You draw a dashed line when the points on that line are not part of the solution.
To determine the line you need to points.
For example, for the line {{{x+y=150}}} (boundary line for {{{x+y>150}}} ),
you can use the points (0,150) and (150,0).
You get by (0,150) by choosing {{{x=0}}} and solving {{{0+y=150}}}<--->{{{y=150}}} for y.
You get by (150,0) by choosing {{{y=0}}} and solving {{{x+0=150}}}<--->{{{x=150}}} for x.
After drawing the line, you decide which side of the line is the solution.
For example, for {{{x+y>150}}} , you know that the side containing point (0,0) is not part of the solution, because
plugging {{{system(x=0, y=0)}}} into {{{x+y>150}}} makes {{{0+0>150}}} which is not true.
On the other hand, point (100,100) is part of the solution, because
plugging {{{system(x=100, y=100)}}} into {{{x+y>150}}} makes {{{100+100>150}}} which is true.
The graph for {{{x+y>150}}} would be the region colored in the graph below.
{{{drawing(300,300,-50,200,-50,200,
grid(0),
graph(300,300,-50,200,-50,200,x+y>151),
line(0,150,10,140),line(20,130,30,120),
line(40,110,50,100),line(60,90,70,80),
line(80,70,90,60),line(100,50,110,40),
line(120,30,130,20),line(140,10,150,0),
line(-10,160,-20,170),line(-30,180,-40,190),
line(160,-10,170,-20),line(180,-30,190,-40)
)}}}
The graph for {{{250x+200y<=44000}}} would be the region colored in the graph below.
{{{drawing(300,300,-100,400,-100,400,
grid(0),
graph(300,300,-100,400,-100,400,250x+200y<=43800),
line(-100,345,256,-100)
)}}}
For your solution, graph you want to merge the two graph.
You also would like to show that
the values for {{{x}}} and {{{y}}} cannot be negative,
so the solution region is the region inside the quadrilateral below, plus the solid boundary lines.
{{{drawing(300,450,-50,200,-25,350,
grid(0),
line(0,220,176,0),
line(0,150,0,220),line(150,0,176,0),
line(0,150,10,140),line(20,130,30,120),
line(40,110,50,100),line(60,90,70,80),
line(80,70,90,60),line(100,50,110,40),
line(120,30,130,20),line(140,10,150,0),
red(circle(100,95,3)),locate(105,100,P(100,95))
)}}}
 
c. Any point in the solution region is a solution.
For example, if 100 adults buy tickets
{{{100+y>150}}}--->{{{y>150-50}}} means more than 50 children attended.
{{{250*100+200y<=44000}}}--->{{{y<=95}}} means no more than 95 children attended.
The point P(100,95), meaning 100 adults and 95 children, 
is on a solid boundary line and is part of the solution