Question

is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? explain.

Explanation:

Step1: Calculate percent increase from 50 to 70

The formula for percent change is $\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100\%$. For increase from 50 to 70: Old Value = 50, New Value = 70. So, $\frac{70 - 50}{50}\times100\%=\frac{20}{50}\times100\% = 40\%$.

Step2: Calculate percent decrease from 70 to 50

For decrease from 70 to 50: Old Value = 70, New Value = 50. So, $\frac{70 - 50}{70}\times100\%=\frac{20}{70}\times100\%\approx28.57\%$.

Step3: Compare the two percentages

40% (increase) is not equal to approximately 28.57% (decrease) because the old values (the bases for percentage calculation) are different (50 vs. 70), so the same absolute change (20) results in different relative (percentage) changes.

Answer:

No, the percent increase from 50 to 70 (40%) is not equal to the percent decrease from 70 to 50 (≈28.57%) because the base values (50 and 70) for calculating the percentage change are different.