The board of trustees of a college has recently approved the installation of 80 new emergency blue lights in three parking lots. The number of lights in each lot will be proportionate to the size of the parking lot, which is to be measured in acres. The total number of acres is 44; so the standard divisor is 44over80≈0.55. The standard quota and rounded quota for each lot is listed in the table below.

LotAcresLot’s Standard QuotaLot’s Rounded QuotaA Lot’s Rounded Quota 15

15÷0.55≈27.27 emergency blue lights Lot’s Rounded Quota 27

B

19

19÷0.55≈34.55 emergency blue lights Lot’s Rounded Quota 35

C

10

10÷0.55≈18.18 emergency blue lights Lot’s Rounded Quota 18

Does the sum of the rounded quota equal the number of lights available?

Provide your answer below:

To determine if the sum of the rounded quotas equals the total number of lights available, let's first sum the rounded quotas for each lot.

Given:
- Lot A's Rounded Quota = 27
- Lot B's Rounded Quota = 35
- Lot C's Rounded Quota = 18

Now, let's calculate the sum of these rounded quotas:

\[
27 + 35 + 18 = 80
\]

Since the sum of the rounded quotas is \(80\), and the total number of lights available is also \(80\), the sum of the rounded quotas **does** equal the number of lights available.

Would you like to delve deeper into any specific detail or have any questions?

Here are 5 related questions you might find interesting:
1. What is the purpose of using a standard divisor in this allocation?
2. How would the allocation change if one lot were slightly larger or smaller?
3. Can you explain the difference between standard quota and rounded quota?
4. What would happen if the total number of emergency blue lights was different?
5. How could we apply this method to another resource allocation problem?

**Tip:** Always double-check your rounding, especially when summing rounded values in resource allocation problems, to ensure the total matches the available resources.

Understand how to allocate 80 emergency blue lights across three parking lots based on their proportional size measured in acres. This problem involves calculating standard and rounded quotas for each lot and ensuring their sum equals the total available lights.

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