1Cademy - Solving a High-Cost Weight Training Bench Cost and Revenue Application Using a System of Equations

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Business Break-Even Point

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Solving a High-Cost Weight Training Bench Cost and Revenue Application Using a System of Equations

We can model manufacturing scenarios with cost and revenue functions to determine the break-even point using a system of equations. For example, if a manufacturer of a weight training bench spends $\$120$ to build each bench, sells them for $\$170$ , and has fixed monthly costs of $\$150{,}000$ , the cost function is $C(x) = 120x + 150{,}000$ . The revenue function is $R(x) = 170x$ . To find the break-even point where costs equal revenue, we solve the equation $120x + 150{,}000 = 170x$ . Subtracting $120x$ gives $150{,}000 = 50x$ , which simplifies to $x = 3{,}000$ . Selling $3{,}000$ benches yields revenue and costs of $\$510{,}000$ , making the break-even point the ordered pair $\left(3{,}000, 510{,}000\right)$ .

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Updated 2026-04-25

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OpenStax Intermediate Algebra

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