Brighton Builders is constructing a new twenty-story office building. The first floor has a large foyer, cafeteria, book store, and business supply store with no office suites. Each of the remaining floors houses office suites, restrooms, and elevators on either side of a halway that runs north and south. A 20-foot elevator bank is in the center with 16-foot restroom areas on either side of the elevator. Each office occupies a 10-foot wall span and a 5-foot door/window casing. The total length of the hallway running north and south is 292 feet.

Question

Formulate an absolute value equation to model the number of east office suites on the north side and the south side of the center of the elevators where north of the center of the elevators is considered positive and south of the center of the elevators is considered negative

Answer 1

Let's assume the number of east office suites on the north side of the center of the elevators is represented by variable x.

On the south side, the number of east office suites can be represented by the negative of x, since the south side is considered negative.

The length of the hallway running north and south is 292 feet, and each office suite occupies a 10-foot wall span and a 5-foot door/window casing. Therefore, the combined length of the office suites on both sides is 10x ft (north side) + 10(-x) ft (south side) = 10x - 10x = 0 ft (since they cancel each other out).

However, there are also restroom areas and elevators on either side of the hallway. The restroom areas on both sides have a length of 16 ft. Hence, the total length of the restroom areas is 16 ft + 16 ft = 32 ft.

Therefore, the equation to represent the length of the hallway is given by:

|0| = |292 - 32|

Simplifying further:

0 = |260|

Since the absolute value of 260 is always 260, the equation can be further simplified to:

0 = 260

So, the resulting absolute value equation to model the number of east office suites on the north and south sides of the center of the elevators is:

|0| = |260|