Answer:
Kathy stood on the middle rung of a ladder There are 20 rungs in the ladder.
Solution:
Let there be ‘x’ rungs in the ladder.
It is given that in the beginning she is standing in the middle of the rung. Let the middle rung be [tex]\frac{x}{2}[/tex]
Now it is given that She climbed up 4 rungs which means she climbed [tex]\frac{x}{2} + 4[/tex] rungs.
Again it is given that she moved down 3 rungs which means she moved down [tex]\left[\left(\frac{x}{2}+4\right)-3\right][/tex] rungs.
Then she moved down [tex]\left(\frac{x}{2}+1\right)[/tex] rungs
Again she climbed 9 rungs up and reaches the top which means she climbed [tex]\left[\left(\frac{x}{2}+1\right)+9\right]=\left(\frac{x}{2}+10\right)[/tex] rungs
Now we can use the following equation to find the number of rungs in the ladder
[tex]\begin{array}{l}{\frac{x}{2}+10=x} \\\\ {\frac{x+20}{2}=x}\end{array}[/tex]
x+20 = 2x
20 = 2x-x
x = 20
Thus the number of rungs in the ladder is 20
