SOLUTION: I would appreciate any help on the below question. I came up with P = -x + 62. I am not sure if this is correct or if it should be P = -x + 104. 1. In this problem, we will an

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Question 172531: I would appreciate any help on the below question. I came up with P = -x + 62. I am not sure if this is correct or if it should be P = -x + 104.

1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).

a. Suppose that a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).
Found 3 solutions by Mathtut, Earlsdon, josmiceli:
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website!
so we have (42,20) and (52,10) as points.....lets find the slope
:
10-20/52-42=-10/10=-1......take any point and use point slope formula
:
y-10=-1(x-52)
:
y-10=-x+52
:
BINGO your right

Answer by Earlsdon(6103)   (Show Source):
You can put this solution on YOUR website!
So you need to write the equation: p = mx+b.
Research has found the when p = $20, then x = 42 and when p = $10 then p = 52, so you have two points ((42, 20) and (52, 10)) that can be used to define the curve (line) and can also be used to generate the equation.
First, find the slope of the line using the two given points where x is the independent variable and p is the dependent variable.
using the given points (42, 20) and (52, 10), make the appropriate substitutions to get:

So you now can write:
To find the value of b, substitute the x- and p-coordinates from either one of the two given points. Let's use (42, 20)
Solving for b, we get:
so now you can write the final equation:

Answer by josmiceli(6786)   (Show Source):
You can put this solution on YOUR website!
I get
Since ,
(1) and
(2)
subtract (2) from (1)

Put this back into (1) or (2)

The equation is

This predicts that they can't sell any tiles if the
price is $62 and they will sell 62 tiles if they
give them away. In reality, they would sell their
entire stock then, so this isn't real-world