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A plot of land doubles in size by adding x meters to the length and x meters to the width of the land. If the original plot had an area of 200 by 300 meters, what is the value of x?

Sagot :

kmatras1
The answer is 100.

The overall area will be the length times the width:

200 times 300 = 60000.

If the plot of land doubles in size, then the resulting area will be 120000. To get to 120000, the question is saying that the same number was added to both 200 and 300, which were then multiplied together. The equation will look like this:

(x+200) times (x+300) = 120000

Now, you will multiply these together in a process called FOIL (which means you multiply the first numbers in each parentheses, then the outside numbers, then the inside numbers, then the last numbers):

x^2 (this means x squared, or x times itself) + 300x + 200x + 600 = 120000

Then, you will add together like terms:

x^2 + 500x + 600 = 120000

Next, you will subtract 120000 from both sides to get 0 on one side of the equation:

x^2 + 500x - 6000 = 0

Next, you will essentially perform the opposite of FOIL (now you're trying to get the right side of the equation into two parentheses):

(x + 600) times (x - 100) = 0  (you can check if this is correct by performing FOIL and making sure that product is the previous equation)

Now, set both of the parentheses equal to 0 and solve:

x + 600 = 0 ----> x = -600
x - 100 = 0 ----> x = 100

Lastly, you will have to choose which value for x satisfies the initial question. Since the question is asking for a value within the real world, a negative answer will not work (you cannot give someone -600 meters of land). So, the answer is 100.
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