An elevator company installs elevators in new buildings. The number of meters of cable needed for an elevator is $12$ times the number of stories in the building plus an extra $15$ meters needed to go into the machinery. Which of the following functions best describes how many meters of cable are needed to install the elevator if there are $s$ stories in the building? $\newline$ Choose $1$ answer: $\newline$ (A) $f(s)=12 s+15$ $\newline$ (B) $f(s)=15 s+12$ $\newline$ (C) $f(s)=12 s+12$ $\newline$ (D) $f(s)=15 s+15$

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Q. An elevator company installs elevators in new buildings. The number of meters of cable needed for an elevator is

12

times the number of stories in the building plus an extra

15

meters needed to go into the machinery. Which of the following functions best describes how many meters of cable are needed to install the elevator if there are

s

stories in the building?

\newline

Choose

1

answer:

\newline

(A)

f(s)=12 s+15

\newline

(B)

f(s)=15 s+12

\newline

(C)

f(s)=12 s+12

\newline

(D)

f(s)=15 s+15

Problem Understanding: Understand the problem. $\newline$ We need to find a function that represents the total meters of cable needed for an elevator in a building with $s$ stories. The problem states that the cable needed is $12$ times the number of stories plus an extra $15$ meters for the machinery.
Mathematical Expression: Translate the problem into a mathematical expression. $\newline$ The total meters of cable is the product of $12$ and the number of stories ( $s$ ), plus an additional $15$ meters. This can be written as: $\newline$ Total meters of cable $= 12 \times s + 15$
Matching the Expression: Match the expression to the correct function. $\newline$ We compare the expression from Step $2$ with the given options: $\newline$ (A) $f(s) = 12s + 15$ $\newline$ (B) $f(s) = 15s + 12$ $\newline$ (C) $f(s) = 12s + 12$ $\newline$ (D) $f(s) = 15s + 15$ $\newline$ The correct function that matches our expression is option (A).