To determine the number of cords in a pile of wood, we can start with the given equation:
[tex]\[
\text{number of cords} = \frac{l \cdot w \cdot h}{128}
\][/tex]
where:
- [tex]\( l \)[/tex] is the length of the pile (in feet),
- [tex]\( w \)[/tex] is the width of the pile (in feet),
- [tex]\( h \)[/tex] is the height of the pile (in feet).
Given the measurements:
- [tex]\( l = 8 \)[/tex] feet,
- [tex]\( w = 32 \)[/tex] feet,
we can substitute these values into the equation. So, the equation for the number of cords becomes:
[tex]\[
\text{number of cords} = \frac{8 \cdot 32 \cdot h}{128}
\][/tex]
Next, we perform the multiplication in the numerator:
[tex]\[
8 \cdot 32 = 256
\][/tex]
So, the equation simplifies to:
[tex]\[
\text{number of cords} = \frac{256 \cdot h}{128}
\][/tex]
To simplify this fraction, we divide both the numerator and the denominator by 128:
[tex]\[
\frac{256 \cdot h}{128} = 2h
\][/tex]
Therefore, the equation that can be used to determine the number of cords in a pile of wood [tex]\( h \)[/tex] feet tall is:
[tex]\[
\text{number of cords} = 2h
\][/tex]
Among the given options, the correct equation is:
[tex]\[
\text{number of cords} = \frac{256 h}{128}
\][/tex]
This is mathematically equivalent to [tex]\(2h\)[/tex].
