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

A system of equations can be used to find the cost function, revenue function, and break-even point for a manufacturing scenario. For example, if a manufacturer of a weight training bench spends $\$15$ to build each bench, sells them for $\$32$ , and has fixed costs of $\$25{,}500$ each month, the cost function is $C(x) = 15x + 25{,}500$ . The revenue function is $R(x) = 32x$ . To find the break-even point, we set costs equal to revenue: $15x + 25{,}500 = 32x$ . Subtracting $15x$ from both sides gives $25{,}500 = 17x$ , so $x = 1{,}500$ . When $1{,}500$ benches are sold, the revenue and costs are both $\$48{,}000$ , meaning the break-even point corresponds to the ordered pair $\left(1{,}500, 48{,}000\right)$ .

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Updated 2026-04-25

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OpenStax Intermediate Algebra

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