To determine the number of centimeters in 1 inch from the given proportional relationship \( 6y = 15.24x \), we start by rewriting the equation to find the value of \( y \) when \( x = 1 \) inch.
We can rearrange the equation as follows:
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Divide both sides by 6: \[ y = \frac{15.24}{6}x \]
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Substitute \( x = 1 \): \[ y = \frac{15.24}{6}(1) \]
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Calculate \( \frac{15.24}{6} \): \[ \frac{15.24}{6} = 2.54 \]
Thus, the number of centimeters in 1 inch is \( 2.54 \) centimeters.
So the answer is 2.54 centimeters.