Final answer:
Nathaniel will use approximately 25 cups of sugar for the large meeting, and will need at least 16 boxes to pack the muffins.
Step-by-step explanation:
To answer the question, we first calculate the amount of sugar needed for the large meeting. Nathaniel normally uses 4 4/5 cups of sugar for one batch. Since he requires 5 1/5 times more muffins than a usual batch for the meeting, we multiply the two amounts to find the total sugar needed:
- Convert mixed numbers to improper fractions: 4 4/5 = 24/5 and 5 1/5 = 26/5.
- Multiply the fractions: (24/5) * (26/5) = 624/25.
- Divide 624 by 25 to convert back to a mixed number: 624/25 = 24 24/25 cups, which is approximately 25 cups (since we can’t have a fraction of a cup when measuring ingredients).
Next, we calculate the number of boxes needed:
- Since each regular batch fills 3 boxes and Nathaniel is making 5 1/5 times a regular batch, we multiply 3 boxes by 5 1/5.
- Convert 5 1/5 to an improper fraction: 5 1/5 = 26/5.
- Multiply the boxes by this fraction: 3 * (26/5) = 3 * 26/5 = 78/5.
- Convert 78/5 to a whole number: 78/5 = 15, with a remainder of 3/5, which means we need at least 16 boxes.
Therefore, the answers are (a) 25 cups of sugar and 16 boxes for packing the muffins.