SOLUTION: The equation S= 5000 + 200x and D=9500 -100x express suppy S and demand D, respectively, for a popular compact disc in terms of its price x (in dollars).
Graph the equations on th
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Graph the equations on th
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Question 202086This question is from textbook Elementary and Intermediate Algebra
: The equation S= 5000 + 200x and D=9500 -100x express suppy S and demand D, respectively, for a popular compact disc in terms of its price x (in dollars).
Graph the equations on the same coordinate system.
What happens to the supply as the price increases?
What happens to the demand as the price increases?
What is the equilibrium price?
Please show your work. This question is from textbook Elementary and Intermediate Algebra
You can put this solution on YOUR website! If you move the x terms in front of the constant terms in both equations, you end up with the Slope-intercept form (y = mx + b) of the equation of a line:
S = 200x + 5000
which tells us the slope, m, is 200 and the y-intercept is 5000 (or the point (0, 5000).
D = -100x + 9500
which tells us the slope is -100 and the y-intercept is 9500. With this information you should be able to graph these lines. (A graph is provided below.)
From the slope of supply equation (or by looking at the graph of the supply equation) we can tell what happens to the supply as the price goes up. Since the slope is positive, as one value (the price) goes up the other value (supply) also goes up.
Similarly the slope of the demand equation is negative. So as the price goes up, the demand will go down.
The equilibrium point is where the supply equals the demand. Graphically this is the point where the lines intersect. Algebraically we can use the fact that if D = S then 200x + 5000 = -100x + 9500. We can solve this equaltion:
Add 100x to both sides:
300x + 5000 = 9500
Subtract 5000 from both sides:
300x = 4500
Divide both sides by 300:
x = 15
This tells us that the equilibrium point is where x = 15. We can find the supply (and demand since they are the same at the equilibrium point) by substituting 15 for x in either the supply or demand equation:
S = 200(15) + 5000
S = 3000 + 5000
S = 8000
The equilibrium point is (15, 8000).
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