Help with Algebra Open-Ended Questions - Linear inequality, graphing, system of equations?

Question

I have a two open ended questions I don't understand on my math homework. We have 20 questions in all so obviously there are some we won't understand. The questions are below.

7. Tickets for a school play cost either $2 or $3, depending on the age of the buyer. The total amount of money brought in was at most $282.

A. Write a linear inequality that describes the situation.
B. Graph the linear inequality.
C. What is the maximum number of tickets that could have been sold for $2?
D. What is the maximum number of tickets that could have been sold for $3?

13. At most 500 ft. of fencing is available for a steer pasture. There is only space for the pasture to be at most 100 ft. wide.

A. Write a system of two linear inequalities that describes this situation.
B. Graph the system to show all possible solutions.
C. Write two possible solutions to the problem.

I appreciate any help you can offer me for these questions.
Thanks in advance.

Answer 1

#7. Let x= tickets sold at $2
y= tickets sold at $3
Then 2x +3y < 282 inequality
To graph, momentarily remove inequation and rearrange to: y = 94-2/3 x. This describes a line with a value of y=94 at x=0 and a -2/3 slope. The line defines the upper bound of the inequality between y=94 and y=0.
From above, you should be able to to find x, the # of $2 tickets. (Hint 282/2)

13. Here there are TWO restrictions, and you have to determine which is the most restricting restriction. They are
The fencing restriction P<500 feet such that 2x+2y<500
AND
The pasture restriction (x= 1 side, y= other side, assume a rectangle) x<100, y<100
The graph: The pasture restriction would be shown by the "inside" of a square located on the xy axis with one corner at the origin, a second corner at y=100,x=0,
a third corner at y=100,x=100, and a last corner at x=100, y=0. The fencing restriction would be shown by the equation 2x +2y < 500. Again, temporarily removing the inequality and rearranging, you get
y = 250-x.
On the xy axis, the line between x=0,y=250 and y=0,x=250 can be drawn. "Inside" this line and the x and y axis is the solution for all rectangle-sized fences that could be prepared. You will note that the pasture restriction is totally within the fencing restriction,
so any pastures with an x or y dimension less than 100 feet can be constructed with the fencing.

Answer 2

read through your textbook.. is hard to sketch the graph here..

Answer 3

well maybe if you them headphones off you can hear and listen in Algebra class!