Question

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 decreased 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 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.

Answer 1

To determine which statement(s) are true, we need to analyze the percentage changes and the corresponding equivalent expressions given in each option.

1. If the number of people who watched the movie decreased by 28%, the new number of viewers can be represented as:
\[
n - 0.28n = 0.72n
\]
This indicates that only 72% of the original audience (n) watched the movie after the decrease.

2. If the number of people who watched the movie decreased by 72%, the new number of viewers can be represented as:
\[
n - 0.72n = 0.28n
\]
This indicates that only 28% of the original audience (n) watched the movie after the decrease.

3. If the number of people who watched the movie increased by 28%, the new number of viewers can be represented as:
\[
n + 0.28n = 1.28n
\]
This indicates that the new audience is 128% of the original (n).

4. If the number of people who watched the movie increased by 72%, the new number of viewers can be represented as:
\[
n + 0.72n = 1.72n
\]
This indicates that the new audience is 172% of the original (n).

Given this analysis, the options can be evaluated as follows:

- **A:** False - Decrease by 28% would result in 72% of n, not \( n - 0.28n \), which equals \( 0.72n \).
- **B:** False - Decrease by 72% would leave you with 28% of n, not \( n - 0.72n \), which equals \( 0.28n \).
- **C:** True - Increase by 28% results in \( n + 0.28n = 1.28n \).
- **D:** True - Increase by 72% results in \( n + 0.72n = 1.72n \).

So, the correct statements are:

**C and D are true.**