Problem 90 - Elementary Algebra

Question

The board designated unrestricted endowment at the Walker Art Center in Minneapolis increased from \(\$ 22,140,129\) in 2009 to \(\$ 27,590,778\) in 2010 . Find the percent increase. Round to the nearest percent. (Source: www.walkerart.org)

Step-by-Step Solution

Answer

The percent increase is approximately 25%.

Step 1 - Identify the initial and final values

The initial value in 2009 is \( 22,140,129 \) dollars and the final value in 2010 is \( 27,590,778 \) dollars.

Step 2 - Calculate the difference

Subtract the initial value from the final value to find the increase: \( 27,590,778 - 22,140,129 = 5,450,649 \)

Step 3 - Calculate the percent increase

Use the formula for percent increase: \[ \text{Percent Increase} = \frac{\text{Increase}}{\text{Initial Value}} \times 100 \] Plugging in the values: \[ \text{Percent Increase} = \frac{5,450,649}{22,140,129} \times 100 \]

Step 4 - Simplify and round the result

Calculate the fraction: \[ \frac{5,450,649}{22,140,129} \approx 0.246 \] Multiply by 100 and round to the nearest percent: \[ 0.246 \times 100 \approx 24.6\rightarrow 25 \]

Key Concepts

percent change

Percent change helps in determining how much a quantity has increased or decreased over time, typically presented as a percentage. It is useful for comparing changes in different contexts. To calculate the percent change, you subtract the initial value from the final value to find the difference. Then, divide this difference by the initial value and multiply the result by 100. This gives you the percent change. For instance, in the problem provided, the formula used is: \[ \text{Percent Increase} = \frac{\text{Increase}}{\text{Initial Value}} \times 100 \]

initial value

The initial value is the starting point or the value at the beginning of the observation period. Knowing the initial value is crucial for calculating percent change. In the given problem, the initial value is the amount of the unrestricted endowment at the Walker Art Center in 2009, which is \(22,140,129\) dollars. By identifying the initial value, you can then accurately determine how much it has increased or decreased over time.

final value

The final value represents the ending point or the value at the end of the observation period. This is the value against which you will measure the change from the initial value. For our specific problem, the final value is the amount of the endowment at the Walker Art Center in 2010, recorded as \(27,590,778\) dollars. Having this value lets you calculate the overall change and subsequently the percent increase.

fraction decimal conversion

When calculating percent change, you often need to convert fractions to decimals for easier handling. For example, if you need to determine the percent increase, you might end up with a fraction like \( \frac{5,450,649}{22,140,129} \). Converting this fraction into a decimal is done by dividing the numerator (5,450,649) by the denominator (22,140,129), which approximately equals 0.246. To find the percent change, multiply the decimal by 100, resulting in 24.6, which can be rounded to 25 percent.