To evaluate the expression \(\frac{b + 3c}{a}\) for \(a = 3\), \(b = 6\), and \(c = 4\), we first substitute the values into the expression:
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Substitute \(b\) and \(c\): \[ \frac{6 + 3 \cdot 4}{3} \]
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Calculate \(3 \cdot 4\): \[ 3 \cdot 4 = 12 \]
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Add this result to \(b\): \[ 6 + 12 = 18 \]
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Now substitute this back into the expression: \[ \frac{18}{3} \]
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Now calculate \(\frac{18}{3}\): \[ 18 \div 3 = 6 \]
Thus, the final answer is:
\[ \boxed{6} \]