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.

Question

0.72n

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.

Answer 1

To determine which set of statements is true, let's analyze the given expression and its meaning.

Last Friday, the number of people who watched the movie was \( n \). This Friday, the number of people who watched the same movie is represented by \( 0.72n \).

Let's break this down:

• \( 0.72n \) indicates that the current number of viewers is 72% of \( n \). This can also be interpreted as a decrease in the number of viewers from last Friday since \( 0.72 \) is less than \( 1 \).

To find the percentage decrease:

• The decrease in viewers is \( n - 0.72n \), which simplifies to \( 0.28n \).
• This means there is a decrease of \( 0.28n \), which corresponds to a percentage decrease of \( 28% \).

Now let's analyze each option:

A. The number of people who watched the movie at the theater increased by 28%. An equivalent expression that represents this situation is \( n + 0.28n \).
(This statement is false; it indicates an increase rather than a decrease.)

B. The number of people who watched the movie at the theater decreased by 72%. An equivalent expression that represents this situation is \( n − 0.72n \).
(This statement is false; the decrease is 28%, not 72%.)

C. The number of people who watched the movie at the theater increased by 72%. An equivalent expression that represents this situation is \( n + 0.72n \).
(This statement is false; it indicates an increase rather than a decrease.)

D. The number of people who watched the movie at the theater decreased by 28%. An equivalent expression that represents this situation is \( n − 0.28n \).
(This statement is true; there is indeed a decrease of 28%.)

Therefore, the correct answer is D: The number of people who watched the movie at the theater decreased by 28%. An equivalent expression that represents this situation is \( n − 0.28n \).