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Question 141302This question is from textbook
: Juan and his friends are going to an amusement park and discover that they have two ticket options. One option is to buy an admission ticket for $5.00 and then payfor each ride. The other option is to buy an admission ticket for $2.00 and then pay a ride. What do you think Juan should do?
a) How much does Juan spend if he buys the $5.00 admission ticket and goes on eight rides? 12 rides? 20 rides? 0 rides? x rides?
b) How much does he spend if he buys the $2.00 admission ticket and goes on eight rides? 12 rides? 20 rides? 0 rides? x rides?
c) Let x represents the number of rides and y represent the total amount spent in dollars. Use the expressions for x rides in parts (a) and (b) to write two equations to represent the two admission and ticket options. Since y stands for the total Juan spends, start your equations with "y = ".
d) Graphboth admissions options on the same axes. Scale the x–axis one unit per ride, for up to 20 rides. Scale the vertical axis one unit per dollar, for up to $20.00. Label each line as to which admission option it represents.
e) Use the graph from part (d) to find the point of intersection for the graphs of the two options. What does that point represent? How much will Juan spend at that point?
f) Use substitution to solve your equations from part (c). Refer to problem WR–41 if you need help. Compare the equation results with your solution by graphing in part (e).
g) Write an explanation to Juan as to what ticket option he should choose. Include enough information so that he can make an informed decision.
h) If you were going to this amusement park, what option would you choose? Explain.
This question is from textbook
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! 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.
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