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Digital SAT
Digital SAT Mathematics - Calculator Section

Equilibrium Price Calculation in Demand and Supply

Very Hard Functions And Modeling Linear, Quadratic, And Exponential Models

A company manufactures and sells a certain product. The demand function for the product is given by the equation:

$$ D(x) = 150 - 3x $$

where $D(x)$ is the number of units demanded, and $x$ is the price per unit in dollars. The supply function for the same product is given by:

$$ S(x) = 2x + 50 $$

where $S(x)$ is the number of units supplied. To find the equilibrium price, we need to set the demand equal to the supply:

$$ D(x) = S(x) $$

Determine the equilibrium price and calculate the value of $x$ that represents this price.

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