Algebra Demystified 2nd Ed

392 algebra De mystif ieD

EXAMPLES

Represent the revenue formula in terms of x, the number incremental

changes in the price.

A department store sells 20 music players per week at $80 each. The man-

ager believes that for each decrease of $5 in the price, six more players

will be sold.

Let x represent the number of $5 decreases in the price. Then the price will

decrease by 5x: P = 80 – 5x.

The sales level will increase by six for each $5 decrease in the price—the

sales level will increase by 6x: Q = 20 + 6x.

Thus, R = PQ becomes R = (80 – 5x)(20 + 6x).

A rental company manages an office complex with 16 offices. Each office

can be rented if the monthly rent is $1000. For each $200 increase in the

rent, one tenant will be lost.

Let x represent the number of $200 increases in the price.

P = 1000 + 200x Q = 16 – 1x R = (1000 + 200x)(16 – x)

A grocery store sells 300 pounds of bananas each day when they are priced

at 45 cents per pound. The produce manager observes that for each 5-cent

decrease in the price per pound of bananas, an additional 50 pounds are

sold. Let x represent the number of 5 cent decreases in the price.

P = 45 – 5x Q = 300 + 50x R = (45 – 5x)(300 + 50x)

(The revenue will be in cents instead of dollars.)

A music storeowner sells 60 newly released CDs per day when the price is

$12 per CD. For each $1.50 decrease in the price, the store will sell an additional

16 CDs each week. Let x represent the number of $1.50 decreases in the price.

P = 12.00 – 1.50x Q = 60 + 16x R = (12.00 – 1.50x)(60 + 16x)

PRACTICE

Let x represent the number of increases/decreases in the price.

1. The owner of an apartment complex knows he can rent all 50 apart-
   ments when the monthly rent is $400. He thinks that for each
   $25 increase in the rent, he will lose two tenants.
   P = __
   Q = __ R = __

EXAMPLES

Represent the revenue formula in terms of

changes in the price.

A department store sells 20 music players per week at $80 each. The man-

EXAMPLES

Represent the revenue formula in terms of

PRACTICE

Let xxx represent the number of increases/decreases in the price. represent the number of increases/decreases in the price.

1. The owner of an apartment complex knows he can rent all 50 apart-
   ments when the monthly rent is $400. He thinks that for each

PRACTICE

Let