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

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
`(x)/(2)`

Now it is given that She climbed up 4 rungs which means she climbed
`(x)/(2) + 4` rungs.

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

Then she moved down
`\left((x)/(2)+1\right)` rungs

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

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

`\begin{array}{l}{(x)/(2)+10=x} \\\\ {(x+20)/(2)=x}\end{array}`

x+20 = 2x

20 = 2x-x

x = 20

Thus the number of rungs in the ladder is 20