SOLUTION: 2. The state fair is coming to town. Since you love the rides, you can�t wait to go. When you get to the ticket counter you notice three options for purchasing tickets. Option 1:

Question 111542: 2. The state fair is coming to town. Since you love the rides, you can�t wait to go. When you get to the ticket counter you notice three options for purchasing tickets.
Option 1: Pay one price at the gate for limitless riding�$25
Option 2: Pay $5 at the gate and then paying $0.75 for each ride you go on.
Option 3: Pay nothing at the gate and pay $1.25 for each ride.
Write general linear equations for each option that describe your cost (y) as a function of how many rides you go on (x)
(use y = mx + b form)
Also, if you knew ahead of time that you were going to experience 17 rides, which option would be cheapest?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
To write the equations, realize that y will be the amount of money paid and x will be the number of rides.
:
Option 1: , because whether you go on 0 or 100 rides, the cost is the same.
:
Option 2: , because .75 = 3/4 and you have the initial $5 cost.
:
Option 3: , 1.25 = 5/4
:
Now, evaluating each option for 17 rides:

(I used a calculator)

:
Option 2 is the cheapest.
:
You should get extra credit for this next part:
:

The horizontal line is option 1, the green line is option 2, and the blue line is option 3.
:
Option 3 is a good deal if you aren't going on more than 9 rides. If you go on 10 rides, Option 3 and Option 2 cost the same.
:
If you are going to ride 11 times or more up to 26 times, then Option 2 is the best deal.
:
Option 1 isn't a good deal unless you are going to go on 27 rides or more.
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