The reason the percent increase from 45 to 75 is not equal to the percent decrease from 75 to 45 can be explained by the following options:
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The amount of change is different for the percent increase and the percent decrease.
- The amount of change is \(75 - 45 = 30\) for the increase and \(75 - 45 = 30\) for the decrease, but this alone doesn't clarify the percentage, as it needs to be compared to different bases.
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The ratio of the percent increase is not the same as the percent decrease.
- Percentages are calculated based on the original values, so the ratio resulting in a percentage will differ.
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The ratio for the percent increase has a smaller denominator than the percent decrease.
- For the increase, the base (denominator) is 45, and for the decrease, it's 75. The same change (30) is divided by a smaller base (45) for the increase, resulting in a larger percentage.
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The ratio for the percent increase has a different numerator than the percent decrease.
- Actually, the numerator (the amount of change) is the same (30) for both calculations.
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The original amount for the percent increase is different from the original amount for the percent decrease.
- This is correct; the original amount differs for the two situations (45 for increase, 75 for decrease), which affects the percentage calculations.
Thus, the three correct options that explain why the percent increase is not equal to the percent decrease are:
1, 2, and 5.