Solution: Let $ h $ represent the number of hours worked. The total fee for the first consultant is $ 300 + 75h $, and for the second consultant it is $ 200 + 90h $. Setting these equal:
["Solving When Two Consulting Fees Are Equal: Find the Hours Worked Using Equation $ 300 + 75h = 200 + 90h $", "When working with multiple consultants, one common dilemma is determining the number of hours needed for both to earn the same total fee. In real-world billing scenarios, this helps clients and businesses find a fair point where both parties agree—especially when one consultant charges a flat rate plus hourly rate, and the other has a different pricing structure.", "Suppose Consultant A charges:\n$$\n\ ext{Fee}_A = 300 + 75h\n$$\nand Consultant B charges:\n$$\n\ ext{Fee}_B = 200 + 90h\n$$\nwhere $ h $ represents the number of hours worked. To find when both consultants earn the same total fee, set the two expressions equal:", "$$\n300 + 75h = 200 + 90h\n$$", "### Step-by-Step Solution", "1. Subtract $ 75h $ from both sides:\n$$\n300 = 200 + 15h\n$$", "2. Subtract 200 from both sides:\n$$\n100 = 15h\n$$", "3. Divide both sides by 15:\n$$\nh = \frac{100}{15} = \frac{20}{3} \approx 6.\overline{6}\n$$", "### Interpretation", "The fees are equal when each consultant works $ \frac{20}{3} $ hours, or approximately 6 hours and 40 minutes. At this point, their total earnings match exactly under the given pricing models.", "### Why This Matters for Clients and Businesses", "Knowing the break-even hour point helps teams negotiate fees, plan budgets, and ensure fairness. Whether you're a freelancer or managing a client project, understanding where two pricing models intersect enables smarter financial decisions.", "Final Note:\nUse the equation $ 300 + 75h = 200 + 90h $ as a quick tool to find the exact hour threshold where both consultants earn the same amount. Computing $ h = \frac{20}{3} $ shows it’s reached just before 7 hours—ideal for forecasting workload costs or calculating break-even time.", "---", "Keywords: consultant pricing, break-even hours, equal fee calculator, $300+75h vs 200+90h, hourly vs flat rate comparison, pricing balance point, real-world billing solution, coding word problems."]
