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Max is considering adding an indoor herb garden in the kitchen. The main herb, basil, is expected to grow at the rate of [tex]3 \frac{5}{8}[/tex] inches per month. To keep it from overgrowing, he wants to calculate its growth. How much will the basil have grown in [tex]5 \frac{1}{2}[/tex] months?

Select one:
A. [tex]19 \frac{15}{16}[/tex] inches
B. [tex]15 \frac{7}{8}[/tex] inches
C. [tex]24 \frac{7}{8}[/tex] inches
D. [tex]22 \frac{7}{8}[/tex] inches



Answer :

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.