For individual or collaborative investigationIf p units of an item are sold for x dollars...

For individual or collaborative investigation

If p units of an item are sold for x dollars per unit, the revenue is px. Use this idea to analyze the following problem.

Number of Apartments Rented  The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial Considerations Currently, the revenue from the complex is $35,000. How many apartments are rented?

Solve the equation from Exercise 54 and answer the question in the problem.

Exercise 54

For individual or collaborative investigation

If p units of an item are sold for x dollars per unit, the revenue is px. Use this idea to analyze the following problem.

Number of Apartments Rented  The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial Considerations Currently, the revenue from the complex is $35,000. How many apartments are rented?

According to the problem, the revenue currently generated is $35,000. Write a quadiatic equation in standard form using your expression from Exercise 53.

Exercise 53

For individual or collaborative investigation

If p units of an item are sold for x dollars per unit, the revenue is px. Use this idea to analyze the following problem.

Number of Apartments Rented  The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial Considerations Currently, the revenue from the complex is $35,000. How many apartments are rented?

Use the answers in Exercises 51 and 52 to write an expression that defines the revenue generated when there are x increases of $20 over $300.

Exercises 51

For individual or collaborative investigation

If p units of an item are sold for x dollars per unit, the revenue is px. Use this idea to analyze the following problem.

Number of Apartments Rented  The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial Considerations Currently, the revenue from the complex is $35,000. How many apartments are rented?

Suppose that x represents the number of $20 increases over $300. Represent the number of apartment units that will be rented in terms of x.

Exercises 52

For individual or collaborative investigation

If p units of an item are sold for x dollars per unit, the revenue is px. Use this idea to analyze the following problem.

Number of Apartments Rented  The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in rent over $300. Furthermore, the manager must keep at least 30 units rented due to other financial Considerations Currently, the revenue from the complex is $35,000. How many apartments are rented?

Represent the rent per unit in terms of x.