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Question: if 6/k=24/k+30 what is the value of k/6?

To solve the equation \(\frac{6}{k} = \frac{24}{k} + 30\), we'll start by finding the common value of \(k\). First, let's isolate the fractions involving \(k\): \[ \frac{6}{k} = \frac{24}{k} + 30 \] Subtract \(\frac{24}{k}\) from both sides to get the fractions on one side: \[ \frac{6}{k} - \frac{24}{k} = 30 \] Combine the fractions on the left side: \[ \frac{6 - 24}{k} = 30 \] Simplify the numerator: \[ \frac{-18}{k} = 30 \] To isolate \(k\), multiply both sides of the equation by \(k\): \[ -18 = 30k \] Next, solve for \(k\): \[ k = \frac{-18}{30} \] Simplify the fraction: \[ k = \frac{-3}{5} \] Now that we know the value of \(k\), we need to find the value of \(\frac{k}{6}\): \[ \frac{k}{6} = \frac{\frac{-3}{5}}{6} = \frac{-3}{5} \times \frac{1}{6} = \frac{-3}{30} = \frac{-1}{10} \] So, \(\frac{k}{6}\) is \(\frac{-1}{10}\).

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