Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 395

If x = 2, the price for each player is P =  80 –  52 () $=  70.

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)

What should the monthly rent be if the rental company needs $20,800 each
month in revenue?

R = (1000 + 200x)(16 – x)

20,800 = (1000 + 200x)(16 – x)

20,800 = 16,000 + 2200x – 200x^2

200 x^2 – 2200x + 4800 = 0

1
200

200 2200 4800 1

200

()xx^2 −+= () 0

x^2 – 11x + 24 = 0

(x – 3)(x – 8) = 0

x – 3 = 0 x – 8 = 0
x = 3 x = 8

If x = 3, the monthly rent will be 1000 + 200(3) = $1600. If x = 8, the monthly
rent will be 1000 + 200(8) = $2600.

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)

What should the price of bananas be for weekly sales to be $140? How
many bananas (in pounds) will be sold at this price (these prices)? (The
revenue will be in terms of cents, so $140 becomes 14,000 cents.)

R = (45 – 5x)(300 + 50x)

14,000 = (45 – 5x)(300 + 50x)

14,000 = 13,500 + 750x – 250x^2

250 x^2 – 750x + 500 = 0