L’production de B est \(2x = 4y\), et B par rapport à C est \(4y:5y\), donc C = \(\frac{5y}{4y} \times 4y = 5y\).

["Title: Analyzing the Relationship Between Variables: Solving (2x = 4y) and (B : C = 4y : 5y) to Find C in Terms of y", "---", "Introduction\nUnderstanding mathematical relationships between variables is essential in algebra, especially when analyzing equations and proportions. This article explores the derivation of ( C = 5y ) based on the equations ( 2x = 4y ) and the ratio ( B : C = 4y : 5y ). We break down the steps to clarify how substitutions and proportional reasoning lead to the final result, supporting better comprehension in math education and problem-solving.", "---", "### Step 1: Simplify the Equation (2x = 4y)", "We start with the linear equation:\n[\n2x = 4y\n]\nTo simplify, divide both sides by 2:\n[\nx = 2y\n]\nThis shows that ( x ) is twice ( y )—a foundational relationship for subsequent calculations.", "---", "### Step 2: Analyze the Ratio ( B : C = 4y : 5y )", "The given ratio of variables ( B ) to ( C ) is expressed as:\n[\n\frac{B}{C} = \frac{4y}{5y}\n]\nAssuming ( y <br/>\neq 0 ), we simplify:\n[\n\frac{B}{C} = \frac{4}{5}\n]\nThus, ( B = \frac{4}{5}C ) (or equivalently, ( C = \frac{5}{4}B )). We now express ( C ) in terms of ( y ).", "---", "### Step 3: Connect ( y ) to ( C ) Using Proportionality", "While ( B ) is tied to ( y ) through ( B = \frac{4}{5}C ), we use the earlier result ( x = 2y ) to contextualize ( y ) in the system. However, since ( B ) and ( C ) are directly proportional relative to ( y ), and no direct dependency on ( x ) is specified beyond this relation, we focus on expressing ( C ) using only the ratio and ( y ). Given that ( \frac{B}{C} = \frac{4}{5} ) and no further dependencies on ( x ), solving directly:", "From ( \frac{B}{C} = \frac{4}{5} ), rearrange:\n[\nC = \frac{5}{4}B\n]\nBut ( B ) itself depends on ( y ), and since the ratio ( 4y : 5y ) normalizes cleanly, we substitute proportional scaling. Recognizing that ( B ) scales with ( 4y ), we see ( C ) scales with ( 5y ) under consistent proportional relationships.", "Thus,\n[\nC = 5y\n]", "---", "### Step 4: Why This Matters — Real-World Applications and Educational Value", "This algebraic derivation exemplifies how proportional relationships in variables support modeling in physics, economics, and data science. Grasping such simple yet powerful linkages empowers learners to tackle more complex equations and systems. The equation ( 2x = 4y ) demonstrates linear scaling, while the ratio ( B : C = 4y : 5y ) embodies proportional reasoning—a core skill in mathematics.", "---", "### Conclusion", "From ( 2x = 4y ), simplified via ( x = 2y ), and the ratio ( B : C = 4y : 5y ) normalized to ( C = 5y ), we conclude that:\n[\nC = 5y\n]\nThis clear, step-by-step breakdown reinforces foundational algebra and supports deeper understanding of variable interdependence. Whether in classroom learning or real-world problem-solving, mastering such equations builds a strong foundation in mathematical reasoning.", "---", "Keywords: algebra, solving equations, proportional reasoning, variable relationships, math education, (2x = 4y), ratio (4y:5y), simplification, scaling variables, mathematical derivation", "Meta Description:\nLearn how to solve (2x = 4y) and use the ratio (B : C = 4y : 5y) to derive (C = 5y). A clear algebra step-by-step guide for students and educators.", "---", "For more in-depth guides on proportional reasoning and linear equations, explore our full algebra resources."]