The concentration of the new solution is \(\frac{3}{15 + x} = 0.10\).

["# Solving the Equation: How to Find (x) in (\frac{3}{15 + x} = 0.10)", "Understanding how to solve equations is essential in fields like science, engineering, and data analysis. One important equation frequently encountered is (\frac{3}{15 + x} = 0.10), which models various real-world problems involving ratios, dispersion, and concentration. In this article, we break down step-by-step how to solve (\frac{3}{15 + x} = 0.10) and explore the significance of the variable (x) in practical applications.", "## What Does the Equation Mean?", "The expression (\frac{3}{15 + x} = 0.10) represents a concentration problem, where the numerator (3) may symbolize a measured amount of substance, and the denominator (15 + x) reflects the total volume, with (x) standing for an unknown quantity—such as an unknown contributing volume, a scaling factor, or a variable adjustment. Solving for (x) allows us to determine the exact value needed to achieve the given concentration of 0.10.", "## Step-by-Step Solution", "To solve (\frac{3}{15 + x} = 0.10), follow these algebraic steps:", "1. Eliminate the fraction by multiplying both sides by (15 + x):\n[\n\frac{3}{15 + x} \ imes (15 + x) = 0.10 \ imes (15 + x)\n]\n[\n3 = 0.10(15 + x)\n]", "2. Distribute the 0.10 on the right-hand side:\n[\n3 = 1.5 + 0.10x\n]", "3. Subtract 1.5 from both sides to isolate the variable term:\n[\n3 - 1.5 = 0.10x\n]\n[\n1.5 = 0.10x\n]", "4. Solve for (x) by dividing both sides by 0.10:\n[\nx = \frac{1.5}{0.10} = 15\n]", "The solution is (x = 15).", "## What Does (x = 15) Mean in Context?", "In real-world applications, plugging (x = 15) back into the original equation confirms its correctness:\n[\n\frac{3}{15 + 15} = \frac{3}{30} = 0.10\n]\nThis means that adding 15 units to 15 units yields a total of 30 units, producing a 10% concentration—critical in solutions, dilutions, or dosage calculations.", "## Why Solving Such Equations Matters", "Equations like (\frac{3}{15 + x} = 0.10) appear in chemistry (e.g., mixing solutions), medicine (calculating dosages), environmental science (concentrations of pollutants), and finance (profit margins). Being able to isolate and solve for unknowns empowers precise decision-making and effective problem-solving across many disciplines.", "## Conclusion", "Solving (\frac{3}{15 + x} = 0.10) straightforwardly yields (x = 15), revealing how a small adjustment scales concentrations accurately. Mastering such algebraic techniques unlocks deeper analytical skills, enabling you to tackle complex real-world challenges with confidence. Whether you’re a student, scientist, or professional, understanding how to resolve equations is a powerful tool in your problem-solving toolkit."]