Answer :
The equilibrium price is approximately 32.
The equilibrium quantity is approximately 1589.
To find the equilibrium quantity, we need to set the quantity demanded equal to the quantity supplied and solve for Q.
The quantity demanded is given by the equation Qd(P) = 3125 - 48P, where P represents the price.
The quantity supplied is given by the equation QS(P) = 149 + 45P.
To find the equilibrium quantity, we need to find the price at which the quantity demanded equals the quantity supplied.
Setting Qd(P) equal to QS(P), we have:
3125 - 48P = 149 + 45P
Let's solve this equation step by step:
First, we can simplify the equation by combining like terms:
3125 = 149 + 45P + 48P
Next, we can further simplify by combining the P terms:
3125 = 149 + 93P
Now, we can isolate the P term by subtracting 149 from both sides of the equation:
3125 - 149 = 149 + 93P - 149
2976 = 93P
Finally, we can solve for P by dividing both sides of the equation by 93:
P = 2976/93
P ≈ 32
So, the equilibrium price is approximately 32.
To find the equilibrium quantity, we can substitute this value of P back into either the quantity demanded or the quantity supplied equation. Let's use the quantity demanded equation:
Qd(P) = 3125 - 48P
Qd(32) = 3125 - 48(32)
Qd(32) ≈ 3125 - 1536
Qd(32) ≈ 1589
Therefore, the equilibrium quantity is approximately 1589.
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