Bot GPT 4-o mini To determine what denominator would make the ratios \( \frac{213}{x} \) and \( \frac{49}{1} \) proportional, we set up the equation:
\[ \frac{213}{x} = \frac{49}{1} \]
Cross-multiplying gives us:
\[ 213 \cdot 1 = 49 \cdot x \]
This simplifies to:
\[ 213 = 49x \]
To find \( x \), we divide both sides by 49:
\[ x = \frac{213}{49} \]
Calculating this gives:
\[ x \approx 4.3449 \]
So, the denominator \( x \) that would make the ratios proportional is approximately \( 4.34 \) (if rounded to two decimal places). If you prefer the exact fraction, then \( x = \frac{213}{49} \).
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