Question 141302
I think you left out some data in your problem statement.  How much do the individual rides cost with the $5 admission and how much with the $2 admission?


Be that as it may, I'll give you some hints for each part of this problem.


a) For each of the given numbers of rides, multiply that number times the cost of one ride, then add $5.  The last one, 'x' rides will come out to be cx + 5, where c is the cost of one ride.


b) Same as a, except that you have a different cost per ride and will add $2 at the end.


c) You have already done the work for this one by completing the 'x' rides part of a) and b).  Just put 'y=' in front of the two expressions you got.


d) You have the equations from part c) -- so just graph them as you would any other linear equations in slope intercept form.


e)  The point of intersection represents the number of rides and the total cost where the choice of options doesn't matter -- the cost is the same either way.


f) To use substitution, take the right sides of each of the equations developed in part c) and set them equal to each other.  Then solve for x.  Once you have a value for x, substitute that value into either equation and calculate y.  Your solution set will be the ordered pair that represents the point of intersection you found in part e).


g) Take the x-coordinate value you determined in part f), call that N.


"Juan,

If you are going to ride less than N rides, buy the $2 admission.
If you are going to ride more than N rides, buy the $5 admission.
If you are going to ride exactly N rides, it doesn't matter which admission option you choose."


(You can leave off that last instruction if N is not an integer.  The point being that you cannot go on a fractional part of a ride, so it will always make a difference which option you choose.)


h) This one is up to you -- whether you like to go on a lot (read more than N) rides or not.