Solve by using a system of equations.
The number x of MP3 players a manufacturer is willing to sell is given by x = 20p − 1500, where p is the price, in dollars, per MP3 player. The number x of MP3 players a store is willing to purchase is given by x = −4p + 900, where p is the price per MP3 player. Find the equilibrium price.
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The equilibrium price is where the two lines meet, namely when the number of units the manufacturer is willing to sell equals the number of units the retailer is willing to buy, both at price p.
So
20p-1500=x=-4p+900
Solve for p to get p=100 (and x=500)
To find the equilibrium price, we need to find the value of p where the number of MP3 players the manufacturer wants to sell is equal to the number of MP3 players the store wants to purchase.
We have the equations:
x = 20p - 1500 (manufacturer's supply)
x = -4p + 900 (store's demand)
Setting these two equations equal to each other, we get:
20p - 1500 = -4p + 900
Now we can solve for p:
20p + 4p = 900 + 1500
24p = 2400
p = 2400/24
p = 100
Therefore, the equilibrium price is $100.