- The first step to calculate the percent increase is to find the difference between the new quantity and the original quantity, which is option B.
- Calculate the difference: \(N - O = \$1,650 - \$1,500 = \$150\).
- Divide the difference by the original quantity: \(\frac{\$150}{\$1,500} = 0.1\).
- Multiply by \(100\%\) to find the final percentage: \(0.1 \times 100\% = 10\%\).
- The first step is B and the percent increase is \(\boxed{10\%}\).
Explanation
- Analysis and First Step Identification
The problem asks us to determine the percent increase when a quantity changes from an original value of \(O = \$1,500\) to a new value of \(N = \$1,650\). The formula to calculate the percent increase is given by \(\text{Percent Increase} = \left( \frac{N - O}{O} \right) \times 100\%\). The first step in this calculation is to determine the absolute change in the quantity, which is the difference between the new value and the original value. By examining the given options:
ASumming the values gives \(1,500 + 1,650 = 3,150\), which is not part of the formula.
BFinding the difference gives \(1,650 - 1,500 = 150\), which is the numerator of our fraction.
CDividing the values gives \(\frac{1,650}{1,500} = 1.1\), which is the ratio of the new value to the original value, not the increase itself.
DFinding the percent the original is of the new value is \(\frac{1,500}{1,650} \approx 0.909\), also not relevant to the standard percent increase formula.
Therefore, the first step is to find the difference between the new quantity and the original quantity, corresponding to option B.
- Calculating the Percent Increase
Now we proceed with the calculation using the identified first step. The difference between the new quantity and the original quantity is \(\$1,650 - \$1,500 = \$150\). Next, we divide this difference by the original quantity to find the fractional increase: \(\frac{\$150}{\$1,500} = 0.1\). Finally, we convert this decimal to a percentage by multiplying by \(100\%\): \(0.1 \times 100\% = 10\%\). Thus, the percent increase is \(10\%\).
Examples
Understanding percent increase is vital in everyday finance. For example, if a store raises the price of a \$20 shirt to \$23, knowing the percent increase allows you to evaluate whether the price hike is reasonable. You would calculate \(\left( \frac{23 - 20}{20} \right) \times 100\% = \left( \frac{3}{20} \right) \times 100\% = 15\%\). This same logic applies to calculating investment returns, tracking inflation, or assessing changes in your monthly budget.