Why is the percent increase from 45 to 75 not equal to the percent decrease from 75 to 45? Select three options.
The amount of change is different for the percent increase and the percent decrease.
The ratio of the percent increase is not the same as the percent decrease.
The ratio for the percent increase has a smaller denominator than the percent decrease.
The ratio for the percent increase has a different numerator than the percent decrease.
The original amount for the percent increase is different from the original amount for the percent decrease.
When discussing percent increases and decreases, it is important to note that percentage change is calculated relative to the starting value (the denominator in the ratio). When you go from a smaller number to a larger number versus going from the larger number to the smaller number, the change in value is indeed the same in terms of absolute value, but the relative change is different because the starting points are different. To determine which of the options are valid:
1. The amount of change is different for the percent increase and the percent decrease.
This statement is inaccurate. The amount of change is the same (in absolute terms), which is 75 - 45 = 45 - 75 = 30. So, this should not be selected.
2. The ratio of the percent increase is not the same as the percent decrease.
This statement is true. The ratio (or fraction) that represents the percent change depends on the starting value (denominator), which is different in the two cases.
3. The ratio for the percent increase has a smaller denominator than the percent decrease.
This statement is true. For the percent increase, the denominator is 45, while for the percent decrease, the denominator is 75. A smaller denominator will yield a larger percentage for the same amount of change.
4. The ratio for the percent increase has a different numerator than the percent decrease.
This statement is not correct. The numerator, which represents the amount of change, is the same (30) for both the increase and the decrease.
5. The original amount for the percent increase is different from the original amount for the percent decrease.
This statement is true. The original amount (or starting point) for the percent increase is 45, while the original amount for the percent decrease is 75. The percentage is calculated relative to this original amount, affecting the resulting percent change.
Therefore, the correct options that explain why the percent increase from 45 to 75 is not the same as the percent decrease from 75 to 45 are:
2. The ratio of the percent increase is not the same as the percent decrease.
3. The ratio for the percent increase has a smaller denominator than the percent decrease.
5. The original amount for the percent increase is different from the original amount for the percent decrease.