# An area reserved for a parking lot is 80 feet long and 77 feet wide. The stalls of the lot are at 90° angles to two one-way aisles. Each aisle is 80 feet by 10 feet. The three areas set aside for the parking spaces are congruent rectangles. Each parking space will be 19 feet by 8 feet. What is the maximum number of parking spaces that will fit in the lot?

Mathematics · High School · Thu Feb 04 2021

Answered on

To determine the maximum number of parking spaces that can fit in the lot, we need to calculate the total available area for parking and then divide it by the area required for each parking space. However, we also need to consider the space taken by the aisles.

First, let's calculate the total area of the parking lot: Total parking lot area = Length × Width = 80 feet × 77 feet = 6,160 square feet

Next, calculate the area taken up by the aisles: Each aisle is 80 feet by 10 feet, and since they are one-way aisles, we assume there are two based on the description: Total area of aisles = Number of aisles × (Length × Width) = 2 × (80 feet × 10 feet) = 1,600 square feet

Subtract the total area of the aisles from the total parking lot area to get the available area for parking spaces: Available area for parking spaces = Total parking lot area - Total area of aisles Available area for parking spaces = 6,160 square feet - 1,600 square feet = 4,560 square feet

Now, find out the area required for each parking space: Area per parking space = Length × Width = 19 feet × 8 feet = 152 square feet

Divide the available area for parking by the area required for each parking space to find the maximum number of parking spaces: Number of parking spaces = Available area for parking spaces / Area per parking space Number of parking spaces = 4,560 square feet / 152 square feet = 30

Therefore, the maximum number of parking spaces that can fit in the lot is 30.

Answered on

To find the maximum number of parking spaces that will fit in the parking lot, we need to calculate the area set aside for parking stalls and divide it by the area of one parking space.

First, we calculate the total area of the parking lot: Total area of the parking lot = Length × Width = 80 feet × 77 feet = 6160 square feet.

Now, we determine the area taken by the aisles: Since there are two aisles, each 80 feet by 10 feet, we calculate the total area of aisles like this: Area of one aisle = Length × Width = 80 feet × 10 feet = 800 square feet. Total area of both aisles = 2 aisles × 800 square feet/aisle = 1600 square feet.

Next, we find out the area reserved for parking stalls by subtracting the aisles' area from the total area of the parking lot: Area reserved for parking stalls = Total area of the parking lot - Total area of the aisles Area reserved for parking stalls = 6160 square feet - 1600 square feet = 4560 square feet.

Now, calculate the area of one parking space: Area of one parking space = Length × Width = 19 feet × 8 feet = 152 square feet.

Lastly, divide the area for parking stalls by the area of one parking space to find the maximum number of spaces: Number of parking spaces = Area reserved for parking stalls ÷ Area of one parking space Number of parking spaces = 4560 square feet ÷ 152 square feet/space ≈ 30 spaces.

So, a maximum of 30 parking spaces will fit in the lot.