Amusement Park and Senior Citizen

A high scoring assessment includes the following:
* All final answers are written as complete sentences.
* Any expression, equations or formulas used need to be clearly stated. * All calculations are performed correctly.
* Specific details in solving or evaluating should be evident. NO WORK, NO CREDIT! * Graphs and visuals are accurate and detailed.

Amusement Parks
Cedar Point Amusement in Sandusky, Ohio, is one of the largest and most popular amusement parks in the world. Over three million people visit the park each year. Opened in 1870, it is the second oldest amusement park in North America. In 1990, Cedar Point was listed in the Guinness Book of World Records for having more roller coasters than any other amusement park in the world. Currently, it has a total of fourteen roller coasters.

In Exercises 1-5, use the following information.
Suppose you, your uncle, and your little brother are purchasing passes to Cedar Point. You pay x dollars for your adult pass and $28 less for your little brother’s pass. Your uncle pays the senior citizen rate, which is $16 less than the adult pass. Two hours after the park opens, 4668 adult passes, 118 senior citizen passes, and 634 child passes are sold. The park’s income for these two hours is $186,320.

1. If the number of people entering the park occurs at a consistent rate, how many people could you expect to be in the park after six hours? After six hours there will be 14,004 adult passes, 354 senior citizen passes, and 1,902 child passes should be in the park. 2. Define variables for each of the unknowns in the problem. Let x represent the cost of an adult pass. The variables are x is Adult Pass cost, x-28 is Child’s Pass cost, x-16 is Senior citizen Pass cost. 3. Using the variables from Exercise 2, write an equation that can be used to model and solve the problem. Using the variables from exercise 2 the equation is 4668x+118(x-16) +634(x-28) =186,320. I got this equation buy multiplying the number of tickets sold in 2 hours of each age group with its variable to equal what the profit is in 2 hours which is $186,320. The solving of the problem I believe is what X equals and X=38.

How I got is first I multiplied 118 to X then to -16 then I did the same and did 634 to X then to -28. After I added 4,668x with 118 xs and 634 xs to get 5,420x, and then added -1888 with -17,752 to get -19,640. I then added 19,640 to 186320 to get 205,960. Last I divided 205,960 by 5,420 and therefore I get the answer 38. 4. Using the equation from Exercise 3, determine the individual prices of an adult pass, a child pass, and a senior citizen pass. An adult pass is 38 dollars, a children’s pass is 10 dollars, and a senior’s pass is 22 dollars. 5. Suppose there is a 20% discount on both senior citizen passes and child passes. Determine the income for the park in the first two hours using this discounted cost. After the 20% discount on both senior citizen and child passes the parks income after 2 hours is 184,532.8 dollars.