- First, calculate the original number by subtracting the increase from the new value: \(550 - 200 = 350\).
- Apply the percent change formula: \(\frac{\text{change}}{\text{original}} \times 100\% = \frac{200}{350} \times 100\%\).
- Simplify the fraction \(\frac{200}{350}\) to \(\frac{4}{7}\), which is approximately \(0.5714\).
- Convert this to a percentage (\(\approx 57\%\)) and identify that the closest option provided is \(55\%\), resulting in an approximate answer of \(\boxed{55\%}\).
Explanation
- Analyzing the Problem and Determining the Percent Change Calculation
The problem states that a new number, \(550\), is \(200\) more than an original number. First, we identify the original number (\(V_{old}\)) by subtracting the difference from the new number:
\[V_{old} = 550 - 200 = 350.\]
The absolute change in value is the difference between the new number and the original number, which is \(200\). To find the percent change, we use the formula:
\[\text{Percent Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\%.\]
Substituting the known values into this formula, we get:
\[\text{Percent Change} = \left( \frac{200}{350} \right) \times 100\%.\]
- Calculating the Percentage and Choosing the Best Answer
Performing the calculation:
\[\frac{200}{350} = \frac{4}{7} \approx 0.5714.\]
Multiplying this by \(100\%\) gives:
\[0.5714 \times 100\% \approx 57.14\%.\]
Comparing this result to the provided options:
A\(175\%\)
B\(33\%\)
C\(55\%\)
While the calculated result of approximately \(57\%\) is not explicitly listed, the closest value among the choices is \(55\%\). In many educational contexts, when options are provided and the calculated result is close to one, that option is the intended answer, likely due to rounding or a minor variation in problem parameters. Thus, we select \(55\%\) as the most appropriate approximation.
Examples
Percent change is a fundamental concept used in finance to track the growth of investments or in retail to calculate markups and discounts. For example, if a store buys an item for \(\$350\) and sells it for \(\$550\), the store manager needs to calculate the profit percentage to evaluate their business performance. By calculating the percent change, the manager can see exactly how much the price has increased relative to the cost, which helps in making informed decisions about pricing strategies and inventory management. Understanding this concept allows anyone to better navigate financial information in their daily life.