To find out how many cups are equivalent to [tex]\(4 \frac{1}{4}\)[/tex] gallons, we can follow these steps:
1. Convert the mixed number to an improper fraction:
[tex]\[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4}
\][/tex]
So, we have [tex]\(\frac{17}{4}\)[/tex] gallons.
2. Know the conversion factor between gallons and cups:
1 gallon is equal to 16 cups.
3. Multiply the improper fraction by the conversion factor:
[tex]\[
\frac{17}{4} \text{ gallons} \times 16 \text{ cups/gallon} = \frac{17 \times 16}{4} \text{ cups}
\][/tex]
4. Simplify the multiplication:
[tex]\[
\frac{17 \times 16}{4} = \frac{272}{4} = 68
\][/tex]
Thus, [tex]\(4 \frac{1}{4}\)[/tex] gallons are equivalent to 68 cups. Therefore, the answer is:
[tex]\[ \boxed{68 \text{ cups}} \][/tex]
