To determine how many cups Kayla can fill with her 20 quart jug of lemonade, we first need to convert the measurement of the cup from mixed number form (2 3/4) to improper fraction form.
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Convert 2 3/4 to an improper fraction: \[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \text{ quarts per cup} \]
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Now, we can calculate how many cups Kayla can fill with 20 quarts of lemonade by dividing the total amount of lemonade by the amount per cup: \[ \text{Number of cups} = \frac{20}{\frac{11}{4}} = 20 \times \frac{4}{11} = \frac{80}{11} \]
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Now, we can perform the division: \[ \frac{80}{11} \approx 7.27 \]
Since Kayla can only fill whole cups, we round down to the nearest whole number. Therefore, she can fill 7 cups.
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