It was given that the length of stretch is directly proportional to the weight. Assuming the length is represented by l and the weight by w, we have the following relationship:
[tex]\begin{gathered} l\propto w \\ \therefore \\ l=kw \end{gathered}[/tex]where k is a constant.
The question gives the following parameters:
[tex]\begin{gathered} when\text{ } \\ w=24 \\ l=12 \end{gathered}[/tex]Therefore, we can calculate the constant to be:
[tex]\begin{gathered} 12=k\cdot24 \\ k=\frac{12}{24} \\ k=\frac{1}{2} \end{gathered}[/tex]Therefore, the relationship will be:
[tex]l=\frac{1}{2}w[/tex]If the weight is increased to 43 pounds, the length will be:
[tex]\begin{gathered} l=\frac{1}{2}\cdot43 \\ l=21.5\approx22\text{ inches} \end{gathered}[/tex]The spring will stretch 22 inches.
