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.
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
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|
Let's denote the number of east office suites on the north side as "x" and the number of east office suites on the south side as "y". To formulate an absolute value equation for this scenario, we need to consider the total length of the hallway and the width taken up by the office suites, restrooms, and elevators.
The total length of the hallway is given as 292 feet. Each office suite occupies a 10-foot wall span and a 5-foot door/window casing, resulting in a total width of 10 + 5 = 15 feet. Therefore, the total width taken up by the office suites, restrooms, and elevators is 15(x + y).
Since the elevator bank is in the center, dividing the length of the hallway into two halves, we can express the absolute value equation as follows:
|y - x| = (292 - 15(x + y))/2
In this equation, we subtract 15(x + y) from 292 to account for the remaining width of the hallway that is not taken up by the office suites, restrooms, and elevators. Then, we divide this difference by 2 to obtain the width on each side of the center.
Finally, taking the absolute value of the difference between the number of east office suites on the south side (y) and the number on the north side (x) will give the equation that models this scenario.
To solve this problem, let's break it down step by step:
1. Determine the total length of the hallway on one side of the center of the elevators. Since the total length of the hallway is 292 feet, the length on one side would be half of that. Therefore, the length on one side is 292/2 = 146 feet.
2. Determine the length occupied by each office suite. According to the given information, each office suite occupies a 10-foot wall span and a 5-foot door/window casing. So, the total length occupied by each office suite is 10 + 5 = 15 feet.
3. Determine the number of office suites that can fit on one side of the center of the elevators. Divide the length of the hallway on one side by the length occupied by each office suite. In this case, the number of office suites is 146/15 = 9.7333 (approximately).
4. Since the number of office suites cannot be fractional, we need to formulate an absolute value equation to model the situation. Let's represent the number of office suites on the north side of the center as "x" and on the south side as "y". We know that x + y = 9.7333.
However, to express this equation in terms of absolute values, we need to consider that the north side is considered positive (x > 0) and the south side is considered negative (y < 0).
So, the absolute value equation can be formulated as |x| - |y| = 9.7333.
This equation represents the relationship between 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 is considered positive and south of the center is considered negative.