Solve problem (See Relating Concepts Exercise 1.)Recycling Aluminum Cans A local group of...

Solve problem (See Relating Concepts Exercise 1.)

Recycling Aluminum Cans A local group of scouts has been collecting old aluminum cans for recycling. The group has already collected 12,000 lb of cans, for which they could currently receive $4 per hundred pounds. The group can continue to collect cans at the rate of 400 lb per day. However, a glut in the old-can market has caused the recycling company to announce that it will lower its price, starting immediately, by $.10 per hundred pounds per day. The scouts can make only one trip to the recycling center. How many days should they wait in order to get $490 for their cans?

Exercise 1

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, working Exercise 2in order.

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?

Exercise 2

Solve the equation from Exercise 3 and answer the question in the problem.

Exercise 3

According to the problem, the revenue currently generated is $35,000. Write a quadratic equation in standard form using your expression from Exercise 4.

Exercise 4

Use the answers in Exercise 5 and 6 to write an expression that defines the revenue generated when there are x increases of $20 over $300.

Exercise 5

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.

Exercise 6

Represent the rent per unit in terms of x.