Kathy stood on the middle rung of a ladder. She climbed up 5 rungs, moved down 2 rungs, and then climbed up 7 rungs. Then she climbed up the remaining 2 rungs to the top of the ladder. How many rungs are there in the whole ladder?

sincsenekdq 2022-09-13 Answered
Kathy stood on the middle rung of a ladder. She climbed up 5 rungs, moved down 2 rungs, and then climbed up 7 rungs. Then she climbed up the remaining 2 rungs to the top of the ladder. How many rungs are there in the whole ladder?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Everett Melton
Answered 2022-09-14 Author has 12 answers
Number of rung of the ladder must be odd, because starts in the middle rung. The number of rungs on the ladder is some number, 2n+1 for some whole number 2.
The middle rung (t):
2 n + 1 2 + 1 2
The start t + 5 2 + 7 + 2 = t + 12 ( 2 n + 1 2 + 1 2 ) + 12 = 2 n + 1 2 n + 1 2 2 n = 1 12 1 2 2 n + 1 4 n 2 = 23 2 2 n + 1 = 23 2 n 1 = 23 2 n = 24 n = 12
Number of rungs ( 2 n + 1 ) = 2 × 12 + 1 = 25
There are 25 rungs on the ladder.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more