Algebra Demystified 2nd Ed

396 algebra De mystif ieD

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250 750 500 1

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( xx^2 –  +  ) =  () 0

x^2 – 3x + 2 = 0

(x – 2)(x – 1) = 0

x – 2 = 0 x – 1 = 0

x = 2 x = 1

If x = 2, the price per pound will be 45 – 5(2) = 35 cents. The number of

pounds sold each week will be 300 + 50(2) = 400. If x = 1, the price per

pound will be 45 − 5(1) = 40 cents and the number of pounds sold each

week will be 300 + 50(1) = 350.

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

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

tional 16 CDs per 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)

What should the price be if the storeowner needs revenue of $810 per week

for the sale of these CDs? How many will be sold at this price (these prices)?

R = (12.00 – 1.50x)(60 + 16x)

810 = (12.00 – 1.50x)(60 + 16x)

810 = 720 + 102x – 24x^2

24 x^2 – 102x + 90 = 0

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24 102 90 1

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( xx^2 –  +  ) =  () 0

4 x^2 – 17x + 15 = 0

(4x – 5)(x – 3) = 0

4 x – 5 = 0 x – 3 = 0

4 x = 5 x = 3

x^ = ^5 = .

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When x = 1.25, the price should be 12 – 1.50(1.25) = $10.13 and the number

sold would be 60 + 16(1.25) = 80. If x = 3, the price should be 12 – 1.50(3) =

$7.50 and the number sold would be 60 + 16(3) = 108.