- Define the original number as \(O\) and use the given condition \(200 = O - 400\) to find that \(O = 600\).
- Calculate the percent change using the formula \(\frac{N - O}{O} \times 100\%\), where \(N=200\) and \(O=600\).
- Determine that the change is \(\frac{200 - 600}{600} \times 100\% = -\frac{2}{3} \times 100\% \approx -66.67\%\).
- Match the result to option (a), which is \(\boxed{a}\).
Explanation
- Determining the Original Number
We start by identifying the variables and the given information. Let the original number be represented by \(O\). We are given that the new number, \(N = 200\), is \(400\) less than the original number \(O\). Mathematically, this relationship is expressed as:
\[N = O - 400\]
Substituting the known value of \(N = 200\) into the equation, we get:
\[200 = O - 400\]
Solving for the original number \(O\), we add \(400\) to both sides:
\[O = 200 + 400 = 600\]
So, the original number is \(600\).
- Calculating the Percent Change
The percent change is defined as the change in value relative to the original value, expressed as a percentage. The formula is:
\[\text{Percent Change} = \left(\frac{N - O}{O}\right) \times 100\%\]
We know \(N = 200\) and \(O = 600\). The change in the number is \(N - O = 200 - 600 = -400\).
Substituting these into the formula, we have:
\[\text{Percent Change} = \left(\frac{-400}{600}\right) \times 100\%\]
Simplifying the fraction \(\frac{-400}{600}\) gives \(\frac{-2}{3}\).
\[\text{Percent Change} = -\frac{2}{3} \times 100\% \approx -66.67\%\]
The negative sign indicates a decrease. The magnitude of the percent change is approximately \(66.67\%\).
- Selecting the Correct Option
Comparing our result of approximately \(66.67\%\) to the given options:
AThe percent change is approximately \(66\%\).
BThe percent change is approximately \(1.5\%\).
CThe percent change is approximately \(0.6\%\).
The result clearly aligns with option (a). Thus, the percent change is approximately \(66\%\).
\[\boxed{a}\]
Examples
Percent change is a fundamental concept used in finance and daily economics. For example, if a store lowers the price of a \$600 television by \$400, the new price becomes \$200. Calculating the percent decrease, which is \(\frac{\$200 - \$600}{\$600} \times 100\% = -66.67\%\), helps consumers and retailers understand the scale of a discount. This same logic applies to tracking changes in company revenue, population growth, or any numerical data that fluctuates over time.