Question

Kathy stood on the middle rung of a ladder. She climbed up 4 ​rungs, moved down 3 ​rungs, and then climbed up 9 rungs. Then she climbed up the remaining 3 rungs to the top of the ladder. How many rungs are there in the whole​ ladder?

Answer 1

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  $\frac{x}{2}$

Now it is given that She climbed up 4 rungs which means she climbed $\frac{x}{2} + 4$ rungs.

Again it is given that she moved down 3 rungs which means she moved down   $\left[\left(\frac{x}{2}+4\right)-3\right]$ rungs.

Then she moved down $\left(\frac{x}{2}+1\right)$ rungs

Again she climbed 9 rungs up and reaches the top which means she climbed $\left[\left(\frac{x}{2}+1\right)+9\right]=\left(\frac{x}{2}+10\right)$ rungs

Now we can use the following equation to find the number of rungs in the ladder

$\begin{array}{l}{\frac{x}{2}+10=x} \\\\ {\frac{x+20}{2}=x}\end{array}$

x+20 = 2x

20 = 2x-x

x = 20

Thus the number of rungs in the ladder is 20