To find the total amount of lemonade Beatrice made, we need to add the two quantities together:
- Convert the mixed numbers to improper fractions:
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For \(7 \frac{2}{3}\): \[ 7 \frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{21 + 2}{3} = \frac{23}{3} \]
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For \(10 \frac{3}{5}\): \[ 10 \frac{3}{5} = \frac{10 \times 5 + 3}{5} = \frac{50 + 3}{5} = \frac{53}{5} \]
- Find a common denominator to add the two fractions:
The denominators are \(3\) and \(5\). The least common multiple of \(3\) and \(5\) is \(15\).
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Convert \(\frac{23}{3}\) to a fraction with a denominator of \(15\): \[ \frac{23}{3} = \frac{23 \times 5}{3 \times 5} = \frac{115}{15} \]
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Convert \(\frac{53}{5}\) to a fraction with a denominator of \(15\): \[ \frac{53}{5} = \frac{53 \times 3}{5 \times 3} = \frac{159}{15} \]
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Add the two fractions: \[ \frac{115}{15} + \frac{159}{15} = \frac{115 + 159}{15} = \frac{274}{15} \]
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Convert \(\frac{274}{15}\) back to a mixed number:
- Divide \(274\) by \(15\): \[ 274 \div 15 = 18 \text{ with a remainder of } 4 \] So, \[ \frac{274}{15} = 18 \frac{4}{15} \]
Thus, the total amount of lemonade Beatrice made is \(18 \frac{4}{15}\).
The answer is: c. 18 4/15.
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