Given the building layout for Store A, Store B, Store C, and Store D, what portion of the shared $6000 security costs should be apportioned to Store A?
Apportioned Cost = $[?]
Answer (1)
Calculate the total floor area: 2500 + 1250 + 625 + 625 = 5000 f t 2 .
Determine the proportion of the total floor area occupied by Store A: 5000 2500 = 0.5 .
Multiply the total security cost by Store A's proportion: $6000 × 0.5 = $3000. − T h esec u r i t ycos t a pp or t i o n e d t o St ore A i s \boxed{$3000}.
Explanation
Understanding the Problem We are given the floor areas of four stores (A, B, C, and D) and the total security cost that needs to be shared among them. Our goal is to determine the portion of the security cost that should be allocated to Store A, based on its floor area.
Calculating Total Floor Area First, we need to calculate the total floor area of all the stores combined. We have:
Store A: 2500 f t 2 Store B: 1250 f t 2 Store C: 625 f t 2 Store D: 625 f t 2
So, the total floor area is: 2500 + 1250 + 625 + 625 = 5000 f t 2
Finding Store A's Proportion Next, we need to find the proportion of the total floor area that belongs to Store A. This is calculated by dividing Store A's floor area by the total floor area:
T o t a l A re a St ore A ′ s A re a = 5000 2500 = 0.5
This means Store A occupies 50% of the total floor area.
Calculating Store A's Apportioned Cost Finally, we multiply the total security cost by the proportion of floor area occupied by Store A to find the security cost apportioned to Store A:
St ore A ′ s C os t = T o t a lC os t × St ore A ′ s P ro p or t i o n St ore A ′ s C os t = $6000 × 0.5 = $3000
Therefore, Store A should be apportioned $$3000 of the total security costs.
Final Answer The portion of the shared $6000 sec u r i t ycos t s t ha t s h o u l d b e a pp or t i o n e d t o St ore A i s $3000.
Examples
Imagine a shopping mall where stores share the cost of security based on their size. If Store A occupies half of the mall's area, it would make sense for them to pay half of the security costs. This ensures that the cost is fairly distributed among the stores, proportional to the space they occupy. This principle can be applied to various scenarios, such as sharing utility bills in a shared office space or dividing maintenance costs in an apartment building.
