Question

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.

Explanation:

1. For percent increase from 45 to 75: The amount of change is \( 75 - 45=30 \), and the original amount is 45. The ratio is \( \frac{30}{45}=\frac{2}{3} \approx 66.67\% \).
2. For percent decrease from 75 to 45: The amount of change is \( 75 - 45 = 30 \), and the original amount is 75. The ratio is \( \frac{30}{75}=\frac{2}{5}=40\% \).
3. Analyzing options:

• "The amount of change is different for the percent increase and the percent decrease." - False, the amount of change is 30 in both cases.
• "The ratio of the percent increase is not the same as the percent decrease." - True, as shown above the ratios are different.
• "The ratio for the percent increase has a smaller denominator than the percent decrease." - The denominator for percent increase ratio is 45, for percent decrease is 75. 45 < 75, so this is True.
• "The ratio for the percent increase has a different numerator than the percent decrease." - False, numerator is 30 in both cases.
• "The original amount for the percent increase is different from the original amount for the percent decrease." - True, original amount for increase is 45, for decrease is 75.

Answer:

• 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 original amount for the percent increase is different from the original amount for the percent decrease.