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Question 944205: Help me, please.
Tickets for a plane cost 250 pesos for adults and 200 pesos for children. The sponsor of the show collected a total amount of not more than 44,000 pesos from more than 150 adults and children who watched the plane.
a. How can you find the possible number of children and adults who watched the plane?
b. Give 4 possible numbers of adults and children who watched the plane. Justify your answers.
c. The sponsor of the tickets realized that if the prices of the tickets were reduced, more people would have watched the plane. If you were the sponsor of the plane, would you reduce the prices of the tickets? Why?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! Let us define variables:
 = number of adults who purchased tickets
 = number of children who had tickets
So,
 = amount (in pesos) collected for all the adult tickets sold
 = amount (in pesos) collected for all the children tickets sold
Since "more than  adults and children" watched the plane, "
Since "The sponsor of the show collected a total amount of not more than  pesos",
 .
a. The mathematical statement (or statements) the represent the given situation is (or are)
.....eq.1
 ......eq.2
b. To graph an inequality, such as , 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  (boundary line for ),
you can use the points ( ,) and (,).
You get by (,) by choosing  and solving  <---> for .
You get by (,) by choosing  and solving  <---> for .
After drawing the line, you decide which side of the line is the solution.
For example, for , you know that the side containing point (0,0) is not part of the solution, because
plugging  into makes  which is  true.
On the other hand, point ( ,) is part  the solution, because
plugging  ,  into makes  which  true.
The graph for would be the region colored in the graph below.
The graph for would be the region colored in the graph below.
For your solution, graph you want to merge the two graph.
You also would like to show that the values for and cannot be negative,so the solution region is the   the quadrilateral below, plus the solid boundary lines.
c. Any point in the solution region is a solution.
For example, if  adults buy tickets
 ---> means more than  children attended.
 ---> means no more than 95 children attended.
The point P(, ), meaning adults and children, is on a solid boundary line and is part of the solution.
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