To evaluate the expression \( c + \frac{2a}{b} \) for the values \( a = 5 \), \( b = 3 \), and \( c = 2 \), we first substitute the values into the expression.
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Substitute \( a \), \( b \), and \( c \):
\[ c + \frac{2a}{b} = 2 + \frac{2 \times 5}{3} \]
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Calculate \( 2 \times 5 \):
\[ 2 \times 5 = 10 \]
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Now substitute back into the expression:
\[ 2 + \frac{10}{3} \]
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To add \( 2 \) and \( \frac{10}{3} \), we convert \( 2 \) into a fraction with a denominator of \( 3 \):
\[ 2 = \frac{6}{3} \]
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Now add the fractions:
\[ \frac{6}{3} + \frac{10}{3} = \frac{6 + 10}{3} = \frac{16}{3} \]
The evaluated expression is
\[ \frac{16}{3} \]
So, the final answer is
\[ \frac{16}{3} \]