Question

128 cubic feet of firewood equals 1 cord of wood. if I have 2432 cubic feet of wood how many cords do I have

Answer 1

Solution:

Given that 128 cubic feet of firewood equals 1 cord of wood, this implies that

$1\text{ cord}\Rightarrow128\text{ ft}^3$

If there are 2432 cubic feet of wood, let y represent the number of cords of wood it contains. This implies that

$y\text{ cord}\Rightarrow2432\text{ ft}^3$

To evaluate the value of y,

$\begin{gathered} 1\text{ cord }\Rightarrow\text{ 128 ft}^3 \\ y\text{ cord}\Rightarrow2432\text{ ft}^3 \\ cross-multiply, \\ y\text{ cord}\times128\text{ ft}^3=1\text{ cord}\times2432\text{ ft}^3 \\ divide\text{ both sides by 128 ft}^3 \\ \frac{y\text{ cord}\times128\text{ ft}^3}{128\text{ ft}^3}=\frac{1cord\times2432ft^3}{128\text{ ft}^3} \\ y=1\text{ cord}\times\frac{2432}{128}=1\text{ cord}\times19 \\ \Rightarrow y=19\text{ cords} \end{gathered}$

Thus, there are 19 cords.