To find the total number of cups of lemonade Beatrice made, we first need to add the two quantities of lemonade together. Here is a step-by-step solution:
1. Convert the mixed numbers to improper fractions:
- The initial quantity of lemonade Beatrice made is [tex]\(7 \frac{2}{3}\)[/tex]. To convert this to an improper fraction:
- Multiply the whole number part by the denominator: [tex]\(7 \times 3 = 21\)[/tex].
- Add the numerator: [tex]\(21 + 2 = 23\)[/tex].
- The improper fraction is [tex]\(\frac{23}{3}\)[/tex].
- The additional quantity of lemonade Beatrice made later is [tex]\(10 \frac{3}{5}\)[/tex]. To convert this to an improper fraction:
- Multiply the whole number part by the denominator: [tex]\(10 \times 5 = 50\)[/tex].
- Add the numerator: [tex]\(50 + 3 = 53\)[/tex].
- The improper fraction is [tex]\(\frac{53}{5}\)[/tex].
2. Convert the improper fractions to decimal form:
- [tex]\(\frac{23}{3} \approx 7.666666666666667\)[/tex].
- [tex]\(\frac{53}{5} = 10.6\)[/tex].
3. Add the two quantities together:
- [tex]\(7.666666666666667 + 10.6 = 18.266666666666666\)[/tex].
4. Write the final result:
- The total number of cups of lemonade Beatrice made is [tex]\(18.266666666666666\)[/tex] cups.
Therefore, Beatrice made a total of approximately [tex]\(18.27\)[/tex] cups of lemonade when rounded to two decimal places.
