To solve the problem, we need to follow these steps:
1. Convert the mixed numbers to improper fractions:
- The height of the wall is [tex]\( 8 \frac{1}{3} \)[/tex] feet.
- Convert this to an improper fraction:
[tex]\[
8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}
\][/tex]
- To represent it as a decimal:
[tex]\[
\frac{25}{3} \approx 8.3333 \, \text{(repeating 3)}
\][/tex]
- The length of the wall is [tex]\( 16 \frac{1}{5} \)[/tex] feet.
- Convert this to an improper fraction:
[tex]\[
16 \frac{1}{5} = \frac{16 \times 5 + 1}{5} = \frac{80 + 1}{5} = \frac{81}{5}
\][/tex]
- To represent it as a decimal:
[tex]\[
\frac{81}{5} = 16.2
\][/tex]
2. Calculate the area of the wall:
- Multiply the height and length:
[tex]\[
\text{Area} = 8.3333 \times 16.2 = 135 \, \text{square feet}
\][/tex]
3. Calculate the area painted blue:
- Marcus paints [tex]\(\frac{1}{3}\)[/tex] of the wall blue:
[tex]\[
\text{Area painted blue} = \frac{1}{3} \times 135 = 45 \, \text{square feet}
\][/tex]
4. Determine the correct answer choice:
- The area painted blue is [tex]\(45\)[/tex] square feet.
So, Marcus will paint [tex]\(45\)[/tex] square feet of the wall blue. Therefore, the correct answer is [tex]\( \boxed{45} \)[/tex].
