Chapter 12.2, Problem 64AYU

To determine

To find: The number of rungs the ladder have and the material needed to make the rungs for the ladder.

Explanation of Solution

The number of rungs for the ladder is calculated as,

  $\begin{array}{c}24=49+\left(n-1\right)\left(-2.5\right)\\ -25=-2.5n+2.5\\ 2.5n=27.5\\ n=11\end{array}$

The total material required is calculated as,

  $\begin{array}{c}{S}_{11}=\frac{11}{2}\left(49+24\right)\\ =401.5\end{array}$

Therefore, the number of rungs are $11$ and the total material required is $401.5\text{inches}$ .