Questions: Supply, Demand, and Market Equilibrium In supply (and demand) problems, N is the number of items the supplier will produce (or the public will buy) if the price of the item is x dollars. For a particular product: The supply equation is: N=2x+387 The demand equation is: N=-7x+558 Supply and demand lines intersect at the equilibrium price. This is the price at which there is neither a surplus nor shortage in the market (supply and demand are equal). Solve this system of equations to determine the point at which the two lines intersect. Give your answer as an ordered pair. The two lines intersect at the point: Write your answer as an ordered pair In this situation, what is the selling price when supply and demand are in equilibrium? When supply and demand are in equilibrium, the selling price per item is What is the number of items in the market when supply and demand are in equilibrium? There are items in the market when supply and demand are in equilibrium.

Supply, Demand, and Market Equilibrium In supply (and demand) problems, N is the number of items the supplier will produce (or the public will buy) if the price of the item is x dollars. For a particular product: The supply equation is: N=2x+387 The demand equation is: N=-7x+558 Supply and demand lines intersect at the equilibrium price. This is the price at which there is neither a surplus nor shortage in the market (supply and demand are equal). Solve this system of equations to determine the point at which the two lines intersect. Give your answer as an ordered pair. The two lines intersect at the point: Write your answer as an ordered pair In this situation, what is the selling price when supply and demand are in equilibrium? When supply and demand are in equilibrium, the selling price per item is What is the number of items in the market when supply and demand are in equilibrium? There are items in the market when supply and demand are in equilibrium.
Transcript text: Supply, Demand, and Market Equilibrium In supply (and demand) problems, $N$ is the number of items the supplier will produce (or the public will buy) if the price of the item is $x$ dollars. For a particular product: The supply equation is: $N=2 x+387$ The demand equation is: $N=-7 x+558$ Supply and demand lines intersect at the equilibrium price. This is the price at which there is neither a surplus nor shortage in the market (supply and demand are equal). Solve this system of equations to determine the point at which the two lines intersect. Give your answer as an ordered pair. The two lines intersect at the point: Write your answer as an ordered pair $\square$ In this situation, what is the selling price when supply and demand are in equilibrium? When supply and demand are in equilibrium, the selling price per item is \$ $\square$ What is the number of items in the market when supply and demand are in equilibrium? There are $\square$ items in the market when supply and demand are in equilibrium.
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Solution

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Solution Steps

To find the equilibrium point, we need to solve the system of equations where the supply equals the demand. This involves setting the supply equation equal to the demand equation and solving for \( x \). Once we have \( x \), we can substitute it back into either the supply or demand equation to find \( N \).

Step 1: Set Up the Equations

We are given the supply and demand equations: \[ N = 2x + 387 \] \[ N = -7x + 558 \]

Step 2: Find the Equilibrium Point

To find the equilibrium point, we set the supply equation equal to the demand equation: \[ 2x + 387 = -7x + 558 \]

Step 3: Solve for \( x \)

Combine like terms and solve for \( x \): \[ 2x + 7x = 558 - 387 \] \[ 9x = 171 \] \[ x = \frac{171}{9} \] \[ x = 19 \]

Step 4: Find the Equilibrium Quantity

Substitute \( x = 19 \) back into either the supply or demand equation to find \( N \): \[ N = 2(19) + 387 \] \[ N = 38 + 387 \] \[ N = 425 \]

Final Answer

\(\boxed{(19, 425)}\)

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