Question

You decide to see if you can ride the elevator to street level (Floor 0) without pushing any buttons. The elevator takes you up 4 floors, down 6 floors, up 1 floor, down 8 floors, down 3 floors, up 1 floor, and then down 6 floors to street level. Write and solve an equation to find your starting floor.

Short answer

The starting floor is the 7th floor.

Step-by-step solution

Represent the Elevator Movements

First, we represent each floor movement. An upward movement in the elevator is represented as a positive number, while a downward movement is represented as a negative number. The upward movements are: +4 floors and +1 floor (twice), and the downward movements are: -6 floors, -8 floors, -3 floors, and -6 floors.

Set up the Equation

Next, we set up the equation. In mathematical terms, starting floor + total movements = 0 (street level). We know all the movements, the only unknown is the starting floor which we can represent as \(x\). So, the equation is: \(x + (4 -6 +1 -8 -3 +1 -6) = 0\)

Solve the Equation

Now, solve the equation for \(x\), which is the starting floor. First, add all the numbers in the parenthesis to get the total movements: \(x + (-7) = 0\). Now solve for \(x\) by adding 7 to both sides of the equation: \(x = 0 + 7\).