How to Solve a Profit Equation in Algebra 2
In Algebra II, you often will be presented with an equation that describes a company's profits as a function of x-values, and asked to determine the break-even point, or the point at which profit will reach a certain level. Regardless of what the question asks, your ability to solve these problems hinges entirely upon your ability to use the information that the problem gives you, and to solve equations.
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Instructions
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Determine what the question is asking you. It may ask you at what point profits become negative, positive or zero. You'll need to write your equation based on which one of these issues the question is asking about.
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Plug the value for the profit into the equation for profit. For example, say that your profit equation, provided by the problem, states that profit, P, equals 2x - 700, in x signifies the costs of inputs or products, gross income is twice that cost and 700 is equal to expenditures. If you want to determine the break-even point, or the point at which profit equals 0, you should set P equal to 0, resulting in the equation 0 = 2x - 700. If you want to determine the point at which profit equals 100, the equation becomes 100 = 2x - 700.
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Solve the equation that you write. The break-even point, for instance, occurs when 700 = 2x, or when 350 = x, indicating that spending $350 on inputs makes it possible to break even. Profit equals 100 when 2x = 800, and x = $400.
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