To calculate how much the basil will have grown in [tex]\( 5 \frac{1}{2} \)[/tex] months, follow these steps:
1. Convert the Growth Rate and Time to Improper Fractions:
- The growth rate of the basil is [tex]\( 3 \frac{5}{8} \)[/tex] inches per month. Converting this to an improper fraction:
[tex]\[
3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8}
\][/tex]
- The time span is [tex]\( 5 \frac{1}{2} \)[/tex] months. Converting this to an improper fraction:
[tex]\[
5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}
\][/tex]
2. Calculate the Growth by Multiplying the Growth Rate by the Time:
- Multiply the two improper fractions:
[tex]\[
\frac{29}{8} \times \frac{11}{2} = \frac{29 \times 11}{8 \times 2} = \frac{319}{16}
\][/tex]
3. Simplify the Result:
- The fraction [tex]\( \frac{319}{16} \)[/tex] represents the growth in inches.
- Converting this fraction to a decimal:
[tex]\[
\frac{319}{16} = 19.9375 \text{ inches}
\][/tex]
4. Find the Closest Option:
- Compare the decimal result to the given options to find the closest match:
- [tex]\( 19 \frac{15}{16} \)[/tex] inches, which is [tex]\( 19 + \frac{15}{16} = 19.9375 \)[/tex]
- [tex]\( 15 \frac{7}{8} \)[/tex] inches, which is [tex]\( 15 + \frac{7}{8} = 15.875 \)[/tex]
- [tex]\( 24 \frac{7}{8} \)[/tex] inches, which is [tex]\( 24 + \frac{7}{8} = 24.875 \)[/tex]
- [tex]\( 22 \frac{7}{8} \)[/tex] inches, which is [tex]\( 22 + \frac{7}{8} = 22.875 \)[/tex]
- The option [tex]\( 19 \frac{15}{16} \)[/tex] inches is exactly [tex]\( 19.9375 \)[/tex] inches, which matches our calculation.
Therefore, the basil will have grown [tex]\( 19 \frac{15}{16} \)[/tex] inches in [tex]\( 5 \frac{1}{2} \)[/tex] months, and this is the correct answer.
