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