008A Sample Final A, Question 13

Question: Set up, but do not solve, the following word problem.
One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?

Foundations:
1) What information are we looking for?
2) What is a useful equation involving the desired information?
3) Are there any other equations we can make using the information at hand?
Answer:
1) We want to know the number of tickets sold.
2) We can form the following equation: # of lawn seats + # of covered pavilion seats = 1500 (total concert tickets sold). In terms of variables: if l = # of lawn seats sold, and p = # of covered pavilion seats sold, l + p = 1500.
3) We also have information about total receipts, and we know the cost of each type of ticket. The amount of money earned from selling lawn tickets is 15l, and the amount of money earned from selling covered pavilion tickets is 25p. The total amount earned from selling tickets is 28,5000, so 15l +28p = 28,500.

Solution:

Step 1:
We have to form two equations. The directions say we do not need to solve, so once we have written the two equations we are done. Before we start with equations we start by defining our variables. Let x = # of lawn seats sold, and p = # covered pavilion seats sold.

Step 2:
Since we are looking for the number of each type of tickets sold, and 1500 tickets total were sold, x + p = 1500.

Step 3:
We also know that the Jazz Festival earned $28,500 form selling tickets. This means 15x + 25p = 28,500.

Final Answer:
Let x = # of lawn seats sold, and p = # of covered pavilion seats sold. Then 15x + 25p = 28,500 and x + p = 1500.

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