is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? explain.
is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? explain.
Answer
Explanation:
Step1: Calculate percent increase from 50 to 70
Percent increase formula: $\frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100%$.
Original value = 50, New value = 70.
Difference = $70 - 50 = 20$.
Percent increase = $\frac{20}{50} \times 100% = 40%$.
Step2: Calculate percent decrease from 70 to 50
Percent decrease formula: $\frac{\text{Original Value - New Value}}{\text{Original Value}} \times 100%$.
Original value = 70, New value = 50.
Difference = $70 - 50 = 20$.
Percent decrease = $\frac{20}{70} \times 100% \approx 28.57%$.
Step3: Compare the two percentages
40% (percent increase) ≠ 28.57% (percent decrease). The base values (50 for increase, 70 for decrease) are different, so the same absolute change (20) results in different percent 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 for calculating the percentage (50 vs. 70) are different.