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Question 1174250: A medical supply company found out that there is a demand on a new brand of alcohol in the market.There was demand for 500mL and 1L with the amount Php 80
and Php130, respectively
A.What is the slope?
B.What is the linear function represent the given problem if x is the number of alcohol and y is the price of alcohol?
C.How much does 750mL cost?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step-by-step.
**Understanding the Data**
* We have two data points:
* (500 mL, Php 80)
* (1000 mL, Php 130)
**A. Finding the Slope**
* Let's use the slope formula: m = (y2 - y1) / (x2 - x1)
* Where:
* (x1, y1) = (500, 80)
* (x2, y2) = (1000, 130)
* Substitute the values:
* m = (130 - 80) / (1000 - 500)
* m = 50 / 500
* m = 1/10 or 0.1
* Therefore, the slope is 0.1 (Php per mL).
**B. Finding the Linear Function**
* We'll use the point-slope form of a linear equation: y - y1 = m(x - x1)
* Using the point (500, 80) and the slope m = 0.1:
* y - 80 = 0.1(x - 500)
* y - 80 = 0.1x - 50
* y = 0.1x - 50 + 80
* y = 0.1x + 30
* Therefore, the linear function is y = 0.1x + 30.
**C. Finding the Cost of 750 mL**
* Substitute x = 750 mL into the linear function:
* y = 0.1(750) + 30
* y = 75 + 30
* y = 105
* Therefore, 750 mL of alcohol will cost Php 105.
Answer by ikleyn(52835)  (Show Source):
You can put this solution on YOUR website! .
A medical supply company found out that there is a demand on a new brand of alcohol in the market.
There was demand for 500mL and 1L with the amount Php 80 and Php130, respectively
(A) What is the slope?
(B) What is the linear function represent the given problem if x is the number of alcohol
and y is the price of alcohol?
(C) How much does 750mL cost?
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The solution by @CPhill is NOT CONSISTENT with the problem's requirements.
Definition of the notion/conception of "demand" in Economics:
In economics, demand is the quantity of a good or service
that consumers are willing and able to buy at a given price.
Simply saying, the amount of goods is in the numerator,
while the money (price) is in the denominator.
The given points are (Php80, 500 mL) and (Php130, 1000 mL).
(A) The slope is m =  =  = 10 mL of the alcohol for 1 Php.
It is the Answer to question A.
(B) The function representing the given problem if x is the amount of alcohol
and y is the price of alcohol 
x = a + my = a + 10y. (1)
Here "a" is the unknown coefficient. To find it, substitute the numbers into the first equation
500 = a + 10*80 (2)
and find
a = 500 - 10*80 = 500 - 800 = -300.
So, the demand equation is
x = -300 + 10y. (4)
It is the Answer to question B.
(C) How much does 750mL cost?
750 = -300 + 10*y ---> 750 + 300 = 10y ---> 1050 = 10y ---> y = 1050/10 = 105.
ANSWER to question (C): 750 mL of alcohol cost Php 105,
which is precisely half-way between Php 80 and Php 130,
exactly as it should be, based on common sense.
Solved.
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This problem is an OBVIOUS TRAP.
The trap is made simply by permutation of letters x and y in the problem's formulation.
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