To simplify the expression \(9(7 \frac{1}{2}) + 3(7 \frac{1}{2})\), we start by converting the mixed number \(7 \frac{1}{2}\) into an improper fraction.
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Convert \(7 \frac{1}{2}\) to an improper fraction: \[ 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \]
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Substituting the fraction into the expression: \[ 9(7 \frac{1}{2}) + 3(7 \frac{1}{2}) = 9\left(\frac{15}{2}\right) + 3\left(\frac{15}{2}\right) \]
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Calculating each term: \[ 9\left(\frac{15}{2}\right) = \frac{135}{2} \] \[ 3\left(\frac{15}{2}\right) = \frac{45}{2} \]
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Adding the two fractions: \[ \frac{135}{2} + \frac{45}{2} = \frac{135 + 45}{2} = \frac{180}{2} = 90 \]
Therefore, the final result is: \[ 9(7 \frac{1}{2}) + 3(7 \frac{1}{2}) = 90. \]
None of the provided responses seem to match the calculation of 90. Please check the original problem or any options given.