Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.

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Understand the phrase "x varies jointly as y and z" means that x is directly proportional to the product of y and z. This can be expressed as an equation involving a constant of proportionality, say k.

Write the joint variation equation as \(x = k \cdot y \cdot z\), where \(k\) is a constant.

To solve the equation for \(y\), isolate \(y\) on one side. Start by dividing both sides of the equation by \(kz\) (assuming \(k \neq 0\) and \(z \neq 0\)):

\[ y = \frac{x}{kz} \]

This equation expresses \(y\) in terms of \(x\), \(k\), and \(z\). If you have specific values for \(x\), \(k\), and \(z\), you can substitute them to find \(y\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Joint Variation

Joint variation describes a relationship where one variable varies directly as the product of two or more other variables. In this case, x varies jointly as y and z means x = kyz, where k is the constant of proportionality.

Formulating Equations from Word Problems

Translating a verbal relationship into an algebraic equation involves identifying variables and their relationships. Here, recognizing 'x varies jointly as y and z' helps write the equation x = kyz, setting the foundation for solving for a specific variable.

Solving for a Variable

Solving for y means isolating y on one side of the equation. Starting from x = kyz, divide both sides by kz (assuming k and z are nonzero) to get y = x / (kz), which expresses y explicitly in terms of x, k, and z.