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Chapter 2: Problem 2

Use the four-step procedure for solving variation problems given on page 417 to solve. \(y\) varies directly as \(x . y=45\) when \(x=5 .\) Find \(y\) when \(x=13\)

Short Answer

Expert verified
\(y = 117\) when \(x = 13\).

Step by step solution

01

Identify the law of variation

The exercise states that \(y\) varies directly as \(x\). This is a direct variation, and the mathematical model of direct variation is \(y = kx\), where \(k\) is the constant of variation.
02

Find the constant of variation

We can find the constant of variation \(k\) by taking the given values of \(y\) and \(x\), \(y = 45\) when \(x = 5\), and substituting into the direct variation model. This gives us \(45 = k * 5\). Solving this equation for \(k\) gives \(k = 45 / 5 = 9\).
03

Use the constant of variation to find the unknown

Now that we know \(k = 9\), we can substitute \(k\) and the given value \(x = 13\) into the direct variation model to find \(y\). Substituting these values gives \(y = 9 * 13 = 117\).

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