Questions: Kathy stood on the middle rung of a ladder. She climbed up 5 rungs, moved down 4 rungs, and then climbed up 7 rungs. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?

Determine the total number of rungs in the ladder based on Kathy's movements.

Initial position

Kathy starts on the middle rung of the ladder. Let the total number of rungs be \( n \). The middle rung is \( \frac{n + 1}{2} \) if \( n \) is odd, or \( \frac{n}{2} \) if \( n \) is even. Since ladders typically have an odd number of rungs, we assume \( n \) is odd, so the middle rung is \( \frac{n + 1}{2} \).

Climb up 5 rungs

After climbing up 5 rungs, Kathy's position is \( \frac{n + 1}{2} + 5 \).

Move down 4 rungs

After moving down 4 rungs, Kathy's position is \( \frac{n + 1}{2} + 5 - 4 = \frac{n + 1}{2} + 1 \).

Climb up 7 rungs

After climbing up 7 rungs, Kathy's position is \( \frac{n + 1}{2} + 1 + 7 = \frac{n + 1}{2} + 8 \).

Climb up the remaining 4 rungs to the top

After climbing up the remaining 4 rungs, Kathy reaches the top of the ladder. Her position is now \( \frac{n + 1}{2} + 8 + 4 = \frac{n + 1}{2} + 12 \). Since this is the top rung, it equals \( n \).

Solve for \( n \)

Set \( \frac{n + 1}{2} + 12 = n \). Multiply both sides by 2 to eliminate the fraction: \( n + 1 + 24 = 2n \). Simplify: \( n + 25 = 2n \). Subtract \( n \) from both sides: \( 25 = n \).

The total number of rungs in the ladder is \( \boxed{25} \).

The total number of rungs in the ladder is \( \boxed{25} \).