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

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System of Linear Equations

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

We can use a system of equations to solve for the cost, revenue, and break-even point in manufacturing applications. For example, a manufacturer of a weight training bench spends $\$105$ to build each bench and sells them for $\$245$ . The manufacturer also has fixed costs each month of $\$7{,}000$ . The cost function is $C(x) = 105x + 7{,}000$ . The revenue function is $R(x) = 245x$ . To find the break-even point, we set costs equal to revenue: $105x + 7{,}000 = 245x$ . Subtracting $105x$ gives $7{,}000 = 140x$ , so $x = 50$ . When $50$ benches are sold, the revenue and costs are both $\$12{,}250$ , meaning the break-even point corresponds to the ordered pair $\left(50, 12{,}250 ight)$ .

Updated 2026-04-25

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OpenStax Intermediate Algebra

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