Let \( x \) be the number of Product B units sold. Then, \( 100 - x \) units are Product A. Revenue equation: \( 50(100 - x) + 70x = 6500 \). Solving: \( 5000 - 50x + 70x = 6500 \) simplifies to \( 20x = 1500 \), so \( x = 75 \).

["Mastering Inventory Sales Modeling: How to Solve for Units Sold Using Linear Equations", "Understanding how to model sales and revenue is essential in both business strategy and operations. In this example, we explore a practical scenario where Let ( x ) represent the number of units sold for Product B, and ( 100 - x ) reflects the units sold for Product A. By setting up and solving a revenue equation, businesses can quickly determine optimal product performance and forecast performance goals.", "This article walks you through the setup, step-by-step solution, and real-world implications of solving for ( x ) in a product sales equation.", "---", "### Setting the Scene: What Do the Variables Mean?", "- Let ( x = ) number of units of Product B sold\n- Then, ( 100 - x = ) number of units of Product A sold (assuming total units sold is 100)\n- Product A sells for $70 per unit\n- Product B sells for $50 per unit\n- Total revenue target is $6,500", "---", "### Building the Revenue Equation", "Total revenue comes from multiplying units sold by their respective prices. Writing the equation:", "[\n\ ext{Revenue from Product A} + \ ext{Revenue from Product B} = \ ext{Total Revenue}\n]", "[\n70(100 - x) + 50x = 6500\n]", "This equation expresses total income in dollars based on unit quantities and pricing.", "---", "### Simplifying the Equation", "Expand and combine like terms:", "[\n70(100 - x) + 50x = 6500\n]\n[\n7000 - 70x + 50x = 6500\n]\n[\n7000 - 20x = 6500\n]", "Now isolate the variable:", "[\n-20x = 6500 - 7000\n]\n[\n-20x = -500\n]\n[\nx = \frac{-500}{-20} = 25\n]", "Wait — correction:\nActually from earlier simplification:\n[\n7000 - 20x = 6500 \implies 20x = 7000 - 6500 = 500 \implies x = \frac{500}{20} = 25?\n]", "This contradicts the claim above—let’s recheck the original setup.", "Ah! There’s a common transcription mix-up. Let’s revalidate:", "Given:\n( 50(100 - x) + 70x = 6500 ) — this assumes Product A is $50, Product B is $70", "Re-solving as stated in the instruction:", "[\n50(100 - x) + 70x = 6500\n]\n[\n5000 - 50x + 70x = 6500\n]\n[\n5000 + 20x = 6500\n]\n[\n20x = 1500\n]\n[\nx = 75\n]", "✅ Correct. So confirming variables:", "- Total units sold = 100\n- ( x = ) units of Product B ($70)\n- ( 100 - x = ) units of Product A ($50)\n- Total revenue target: $6,500\n- Equation: ( 50(100 - x) + 70x = 6500 )", "---", "### Final Calculation", "[\n50(100 - 75) + 70(75) = 50(25) + 70(75) = 1250 + 5250 = 6500\n]", "✅ Verified. When 75 units of Product B are sold (at $70), and 25 units of Product A (at $50), total revenue hits $6,500.", "---", "### Why This Model Matters", "Understanding how to model product revenue helps businesses:", "- Set sales targets based on expected unit mix\n- Forecast revenue given market demand distribution\n- Compare profitability across product lines\n- Optimize inventory by knowing which products drive income", "---", "### Conducting the Calculation in Practice", "Suppose you’re a store manager planning next quarter. If product mix aligns with this model, and projections show 100 units sold distributed in a ( x:100-x ) ratio, solving this equation helps quickly calculate expected earnings without sales data lag.", "---", "### Conclusion", "Solving linear equations grounded in real business scenarios not only sharpens analytical skills but empowers strategic decision-making. Whether adjusting marketing focus or inventory restocking, equations like ( 50(100 - x) + 70x = 6500 ) serve as powerful tools.", "Key Takeaway:\nWhen ( x ) units of Product B sell at $70 and ( 100 - x ) units of Product A sell at $50 yield $6,500 total revenue, solving the equation yields ( x = 75 ). Mastering this model allows businesses to precisely measure and anticipate financial outcomes.", "---", "Keywords: Product sales revenue, solve linear equation sales, inventory modeling, unit mix revenue, scoring revenue equality, business operations example, revenue forecasting, algebra in business, production planning math", "Read more about:\n- How to set up sales equations with variable product mix\n- Using algebra to forecast business performance\n- Real-world applications of linear modeling in retail strategy", "---", "Author’s Note: For accurate revenue forecasting, combine this model with actual market research and historical sales data."]