Sure, let's solve this problem step-by-step.
Given:
- The height of the wall is [tex]\( 8 \frac{2}{5} \)[/tex] feet.
- The length of the wall is [tex]\( 16 \frac{2}{3} \)[/tex] feet.
- Marcus paints [tex]\( \frac{1}{2} \)[/tex] of the wall blue.
### Step 1: Convert the mixed numbers to improper fractions.
Height:
[tex]\[ 8 \frac{2}{5} = 8 + \frac{2}{5} = \frac{40}{5} + \frac{2}{5} = \frac{42}{5} \][/tex]
Length:
[tex]\[ 16 \frac{2}{3} = 16 + \frac{2}{3} = \frac{48}{3} + \frac{2}{3} = \frac{50}{3} \][/tex]
### Step 2: Calculate the area of the wall.
[tex]\[ \text{Area} = \text{Height} \times \text{Length} \][/tex]
[tex]\[ \text{Area} = \left( \frac{42}{5} \right) \times \left( \frac{50}{3} \right) \][/tex]
Multiply the fractions:
[tex]\[ \text{Area} = \frac{42 \times 50}{5 \times 3} \][/tex]
[tex]\[ \text{Area} = \frac{2100}{15} \][/tex]
[tex]\[
\text{Area} = 140 \text{ square feet}
\][/tex]
### Step 3: Calculate the area that is painted blue.
Since Marcus paints [tex]\(\frac{1}{2}\)[/tex] of the wall blue:
[tex]\[ \text{Blue Area} = \frac{1}{2} \times \text{Total Area} \][/tex]
[tex]\[ \text{Blue Area} = \frac{1}{2} \times 140 \][/tex]
[tex]\[ \text{Blue Area} = 70 \text{ square feet} \][/tex]
Thus, the number of square feet that will be painted blue is [tex]\(70\)[/tex].
So the correct answer is:
[tex]\[ \boxed{70} \][/tex]
