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Last Friday, the number of people who watched a new movie at a theater was n. This Friday, the number of people who watched the same movie at the theater can be represented by the given expression.

Which set of statements is true?
A.
The number of people who watched the movie at the theater increased by 28%.
An equivalent expression that represents this situation is n + 0.28n.
B.
The number of people who watched the movie at the theater decreased by 72%.
An equivalent expression that represents this situation is n − 0.72n.
C.
The number of people who watched the movie at the theater increased by 72%.
An equivalent expression that represents this situation is n + 0.72n.
D.
The number of people who watched the movie at the theater decreased by 28%.
An equivalent expression that represents this situation is n − 0.28n.

1 answer

To analyze the statements, we need to understand how the given expressions relate to changes in the number of people who watched the movie.

  1. Understanding percentage increases and decreases:

    • An increase of x% can be represented as \( n + \frac{x}{100} n = n(1 + \frac{x}{100}) \).
    • A decrease of x% can be represented as \( n - \frac{x}{100} n = n(1 - \frac{x}{100}) \).

  2. Analyzing each option:

Option A:

  • "Increased by 28%": The expression should be \( n + 0.28n = n(1 + 0.28) = 1.28n \), which indicates that it increased.
  • This statement is true.

Option B:

  • "Decreased by 72%": The expression should be \( n - 0.72n = n(1 - 0.72) = 0.28n \), which indicates that it decreased significantly.
  • This statement is true.

Option C:

  • "Increased by 72%": The expression should be \( n + 0.72n = n(1 + 0.72) = 1.72n \), which indicates that it indeed increased, but it's falsely claiming a significant increase instead of a decrease.
  • This statement is false.

Option D:

  • "Decreased by 28%": The expression would be \( n - 0.28n = n(1 - 0.28) = 0.72n \), indicating a decrease.
  • This statement is also true.

Now, summarizing:

  • Option A is true (increase of 28%).
  • Option B is true (decrease of 72%).
  • Option C is false (misrepresents the increase).
  • Option D is true (decrease of 28%).

Based on the above analysis:

  • Options A, B, and D are correct regarding their statements, while Option C is incorrect.

If you need to determine which statements are true, it's A, B, and D. However, if you’re looking for the single most informative statement regarding just the increase or decrease of people, then A and C would present opposing scenarios and hence can't both be true at the same time.