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If $ 7500 $ seats out of $ 10,000 $ are occupied. What percentage of the stadium is occupied and what percent is empty.

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Last updated date: 22nd Jul 2024
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Answer
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Hint: Percent or percentage is used in mathematics as the number or ratio which is expressed as a fraction of a hundredth. And this is followed by the sign ‘%’. Percentage has no dimension. Hence it is called dimensionless. Every percentage variable has three possible unknown variables: percentage, part, base.
In this problem number of occupied seats are given as well as total number of seats. Then we can first find the number of vacant seats rather than the percentage of empty seats with respect to total seats.

Complete step by step solution:
Given,
Total number of seats $ T = 10,000 $
Number of seats Occupied $ O = 7500 $
Number of seats empty, $ E = ? $
  $ \Rightarrow Number\,of\,empty\,seats = Total\,seats - Occupied\,seats $
Put the value
  $ \Rightarrow Number\,of\,empty\,seats = 10,000 - 7500 $
  $ \Rightarrow Number\,of\,empty\,seats = 2500 $
Now the percentage of occupied seats are, $ {P_o} $
  $ \Rightarrow {P_o} = \dfrac{{Occupied\,Seats}}{{Total\,Seats}} \times 100 $
Put the value
  $ \Rightarrow {P_o} = \dfrac{{7500}}{{10000}} \times 100 $
Simplify
  $ \Rightarrow {P_o} = 75\% $
Hence the percentage of occupied seats, $ {P_o} = 75\% $ .
Now the percentage of empty seats, $ {P_E} $
  $ \Rightarrow {P_E} = \dfrac{{Empty\,Seats}}{{Total\,Seats}} \times 100 $
Put the value
  $ \Rightarrow {P_E} = \dfrac{{2500}}{{10000}} \times 100 $
Simplify
  $ \Rightarrow {P_E} = 25\% $
 Hence the percentage of empty seats are, $ {P_E} = 25\% $ .
So, the correct answer is “$ {P_E} = 25\% $”.

Note: Percentage is widely used in profit and loss. It is also used to show statistics data to increase or decrease in data by how much percentage. The percentage function takes the form z is equal to the x percent of number y. Taking a percent can be viewed as the same operation as multiplication by a fraction.