Let's solve the problem step by step:
### Step 1: Determine the Height and Length of the Wall
The height of the wall is given as [tex]\( 8 \frac{1}{3} \)[/tex] feet and the length is [tex]\( 16 \frac{1}{5} \)[/tex] feet.
### Step 2: Convert Mixed Numbers to Improper Fractions
First, we will convert these mixed numbers into improper fractions or decimals to make our calculations easier.
- The height [tex]\( 8 \frac{1}{3} \)[/tex] can be converted:
[tex]\[
8 \frac{1}{3} = 8 + \frac{1}{3} = 8 + 0.3333\ldots = 8.3333\ldots \approx 8.333
\][/tex]
- The length [tex]\( 16 \frac{1}{5} \)[/tex] can be converted:
[tex]\[
16 \frac{1}{5} = 16 + \frac{1}{5} = 16 + 0.2 = 16.2
\][/tex]
### Step 3: Calculate the Total Area of the Wall
Next, we will calculate the total area of the wall using the formula:
[tex]\[
\text{Area} = \text{Height} \times \text{Length}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Area} = 8.3333\ldots \times 16.2 = 135.0 \text{ square feet}
\][/tex]
### Step 4: Calculate the Fraction of the Wall Painted Blue
Marcus paints [tex]\( \frac{1}{3} \)[/tex] of the wall blue. We need to find [tex]\( \frac{1}{3} \)[/tex] of the total area of the wall.
[tex]\[
\text{Area painted blue} = \text{Total area} \times \frac{1}{3}
\][/tex]
Substituting the total area we calculated:
[tex]\[
\text{Area painted blue} = 135.0 \times \frac{1}{3} = 45.0 \text{ square feet}
\][/tex]
### Conclusion
Marcus paints 45 square feet of the wall blue. Therefore, the correct answer is:
45
### Final Answer
[tex]\[
\boxed{45}
\][/tex]
