SOLUTION: In 2009, the average price of a laptop was $855 and the average price of a desktop PC was $697. Te average price of a laptop has decreased by about $146 per year and the average pr

Algebra ->  Equations -> SOLUTION: In 2009, the average price of a laptop was $855 and the average price of a desktop PC was $697. Te average price of a laptop has decreased by about $146 per year and the average pr      Log On


   

Question 967196: In 2009, the average price of a laptop was $855 and the average price of a desktop PC was $697. Te average price of a laptop has decreased by about $146 per year and the average price of a PC has decreased by about $80. Let L(t) and D(t) be the average prices (in dollars) of laptops and desktop PC's respectively, both at t years since 2009.
Find an equation of L and D.
L(t) =
D(t) =
Use the models to predict in what yrs the avg price of a laptop will be less than the avg price of a desktop PC

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
T = number of years.

L(T) = 855 - 146 * T
D(t) = 697 - 80 * T

you want to know when L(T) will be less than D(T).

equation is L(T) < D(T) which becomes 855 - 146 * T < 697 - 80 * T.

subtract 697 from both sides of the equation and add 146 to both sides of the equation to get:

855 - 697 < 146 * T - 80 * T

combine like terms to get 158 < 66 * T

divide both sides of the equation by 66 to get 2.393939394 < T.

this is the same as T > 2.393939394.

the price of the laptop will be less than the price of the desktop in 2.393939394 years.

let's assume 2.4 years to test this out.

L(T) = 855 - 146 * T becomes 855 - 146 * 2.4 which is equal to 504.6.
D(t) = 697 - 80 * T becomes 697 - 80 * 2.4 which is equal to 505.

the laptop has become cheaper than the desktop when T is greater than 2.393939394 years.