PSAT Math Grid-Ins Question 148: Answer and Explanation
Question: 148
A lamp business uses the following equations to express supply and demand as a function of price and quantity for its lamps:
Supply: Price = 30 - Quantity
Demand: Price = 10 + 3 × Quantity
How many lamps does the business need to sell in order for the supply of lamps to equal the demand for lamps exactly, i.e., for the supply and demand to be at equilibrium?
Correct Answer: 5
Explanation:
5 Since the supply and demand are at equilibrium, set the two expressions equal to one another and solve for the number of lamps:
30 - Quantity = 10 + 3 × Quantity
20 = 4 × Quantity
5 = Quantity
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