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.

0.72n

Which set of statements is true?
A.
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.
B.
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.
C.
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.
D.
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.

1 answer

To analyze the situation, we need to understand what the expression \(0.72n\) represents in relation to the original number of viewers \(n\).

  1. Identify the change: The number of viewers on this Friday is \(0.72n\), which indicates that it is 72% of last Friday's number of viewers \(n\).
  2. Calculate the decrease: Since the number of viewers decreased from \(n\) to \(0.72n\), we can find the decrease:
    • The decrease in the number of viewers is \(n - 0.72n = 0.28n\), which represents a decrease of 28% of \(n\).

Now, we can analyze the provided options:

A. The number of people who watched the movie at the theater decreased by 72%. An equivalent expression that represents this situation is \(n - 0.72n\).

  • Incorrect: The number decreased by 28%, not 72%.

B. The number of people who watched the movie at the theater decreased by 28%. An equivalent expression that represents this situation is \(n - 0.28n\).

  • Correct: The number did decrease by 28%, and the expression for the decrease is \(n - 0.72n = 0.28n\).

C. The number of people who watched the movie at the theater increased by 28%. An equivalent expression that represents this situation is \(n + 0.28n\).

  • Incorrect: There was no increase; the number decreased.

D. The number of people who watched the movie at the theater increased by 72%. An equivalent expression that represents this situation is \(n + 0.72n\).

  • Incorrect: The number did not increase.

Therefore, the true statement is:

B. The number of people who watched the movie at the theater decreased by 28%. An equivalent expression that represents this situation is \(n - 0.28n\).