A wall in Marcus's bedroom is [tex]8 \frac{2}{5}[/tex] feet high and [tex]18 \frac{1}{3}[/tex] feet long. If he paints [tex]\frac{1}{2}[/tex] of the wall blue, how many square feet will be blue?

A. [tex]72 \frac{1}{15}[/tex]
B. 77
C. [tex]144 \frac{1}{15}[/tex]
D. 154



Answer :

To determine how many square feet of the wall Marcus painted blue, let's follow these steps:

1. Convert Mixed Fractions to Improper Fractions:
- The height of the wall is [tex]\( 8 \frac{2}{5} \)[/tex] feet.
- Convert this to an improper fraction:
[tex]\[ 8 \frac{2}{5} = 8 + \frac{2}{5} = \frac{8 \cdot 5 + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5} = 8.4 \text{ feet} \][/tex]
- The length of the wall is [tex]\( 18 \frac{1}{3} \)[/tex] feet.
- Convert this to an improper fraction:
[tex]\[ 18 \frac{1}{3} = 18 + \frac{1}{3} = \frac{18 \cdot 3 + 1}{3} = \frac{54 + 1}{3} = \frac{55}{3} = 18.333\ldots \text{ feet} \][/tex]

2. Calculate the Total Area of the Wall:
- Multiply the height by the length to find the area:
[tex]\[ \text{Total Area} = 8.4 \text{ feet} \times 18.333\ldots \text{ feet} = 154 \text{ square feet} \][/tex]

3. Calculate the Area Painted Blue:
- Since Marcus paints [tex]\(\frac{1}{2}\)[/tex] of the wall blue, multiply the total area by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \text{Blue Area} = 154 \text{ square feet} \times \frac{1}{2} = 77 \text{ square feet} \][/tex]

Therefore, the area of the wall that Marcus painted blue is [tex]\( \boxed{77} \)[/tex] square feet.