Question

which percent change represents a percent increase?
original amount = 978
new amount = 118
percent change = 87%
original amount = 574
new amount = 678
percent change = 18%
original amount = 1,055
new amount = 1,000
percent change = 5%
original amount = 1,254
new amount = 1,045
percent change = 17%

Explanation:

Step1: Recall Percent Increase Definition

A percent increase occurs when the new amount is greater than the original amount. The formula for percent change is $\text{Percent Change} = \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \times 100\%$. If the result is positive, it's an increase; if negative, a decrease.

Step2: Analyze Each Option

• First Option: Original = 978, New = 118. Since $118 < 978$, this is a decrease (negative percent change).
• Second Option: Original = 574, New = 678. Calculate change: $678 - 574 = 104$. Percent change: $\frac{104}{574} \times 100\% \approx 18\%$ (positive, so increase).
• Third Option: Original = 1055, New = 1000. Since $1000 < 1055$, this is a decrease (negative percent change).
• Fourth Option: Original = 1254, New = 1045. Since $1045 < 1254$, this is a decrease (negative percent change).

Answer:

The option with Original amount = 574, New amount = 678, Percent change = 18% (the second option) represents a percent increase.