Answer to Question #134475 in Algebra for Joseph Se

Question

A manufacturer of graphing calculators has determined that 9,000 calculators per week will be sold at a price of $85 per calculator. At a price of $80, it is estimated that 11,000 calculators will be sold.

1. Determine a linear function that predicts the number of calculators that will be sold per week at a price of x dollars.


2. Use the function to find the cost of using the cellular phone for 13 min in 1 month.

Answer 1

Solution.

A linear function has the following form:

$y=a+b\cdot x$ , where

y - number of calculators that will be sold per week (pieces/week);

x - calculator price ($);

a - constant (pieces/week);

b - constant (pieces/(week⋅$)).

Find constant b by subtraction of formulas:

$9000=a+b\cdot 85$ ;

$11000=a+b\cdot 80$ , where

$9000-11000=a+b\cdot 85-(a+b\cdot 80)$ ;

$-2000=b\cdot 5$ ;

$b=-400$ (pieces/(week⋅$)).

Find constant a:

$9000=a-400\cdot 85$ ;

$a=9000+400\cdot 85=43000$ (pieces/week).

Answer 1: $y=43000-400\cdot x$.

Answer 2: We can't use upper function, because constants must have other dimensions (a must have (min/month) dimension; b must have (min/(month⋅$)) dimension). Accordingly we can use upper function to find only the number of calculators that will be sold per week at a price of x dollars.