To solve the ratio \( \frac{x}{6} = \frac{y}{18} \) given that the new value of \( y = 3 \), we can follow these steps:
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Substitute the value of \( y \) into the equation: \[ \frac{x}{6} = \frac{3}{18} \]
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Simplify \( \frac{3}{18} \): \[ \frac{3}{18} = \frac{1}{6} \]
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Now the equation is: \[ \frac{x}{6} = \frac{1}{6} \]
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To find \( x \), we can cross-multiply or just recognize that since the denominators are the same, the numerators must be equal: \[ x = 1 \]
Thus, the value of \( x \) is \( \boxed{1} \).