Question

A village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. the village plans to increase the length by 30%.
A. what will be the new length of the parking lot?
B. how much greater is the new area?
C. if each cars needs about 288 square feet in a parking lot, will the new parking lot be able to fit 20 more cars than the original parking lot? explain.

Answer 1

Answer:

A: 234 feet

B: 6,480 feet^2

C: No, it is able to fit 22 cars, and 22 is not 20.

Step-by-step explanation:

A:

To get a percentage increase, you multiply whatever you're increasing by 1.%(see that it's 1 point percent, 1 "." %)

So to get the new length, we multiply 180 * 1.30  to get a new length of 234 feet.

B:

To find the old area, we multiply our width * our old length

120 * 180 = 21,600

To find the new area, we multiply our width * our new length

120 * 234 = 28,080

To find how much greater the new area is, we subtract the old area from the new area

28,080-21,600 = 6,480

So the new area is 6,480 feet^2 greater than the old area.

C:

Let's start by seeing how many cars that the new area can fit in the first place. To do this, we'll divide our new area by 288.

28,080/288 = 97.5

We round this down instead of up because we cannot fit 0.5 of a car.

Now we check if 97 is 20 more than 75

97 - 75 = 22

So, here's the weird thing now. The question asks if the parking lot is able to fit "20 more cars," which is technically false, because it can fit 22. But if you believe the problem actually meant "20 cars or more," then the answer would be true. It's up to your own interpretation of the question at this point, but going by just what the question was asking, the answer is false.

Answer 2

Answer:

A) 234 feet

B) Area of new parking lot = 28080 square feet

C) The new parking lot will be able to fit 20 more cars than the original parking lot.

Step-by-step explanation:

We are given the following information:

Length of parking lot = 180 feet

Width of parking lot = 120 feet

Number of cars that can be parked = 75

A) Increase in length  = 30%

New length =

$\text{original length} + 30\%(\text{original length})$

$= 180 + \bigg(\displaystyle\frac{30}{100}\times 180\bigg) = 180 + 54 = 234~feet$

B) New area =

$\text{New length}\times Breadth\\= 234\times 120 \\= 28080~ square~feet$

C) Space required by 1 car = 288 square feet

Number of cars we want to fit = 75 + 20 = 95

Area required =

$\text{Number of cars}\times \text{Space occupied by 1 car}$

$= 95\times 288 = 27360~square~feet$

Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.