Problem 39 - Elementary Algebra

Question

Find the percent of the budget cuts to the Arizona university system that are being cut from the Northern Arizona University budget. Round to the nearest percent. Arizona Gov. Jan Brewer recently signed a bill that cuts \(\$ 141.5\) million from the budgets of the Arizona university system; \(\$ 20.5\) million will be cut from NAU (Northern Arizona University). (Source: www.jackcentral.com, Feb. 12, 2008)

Step-by-Step Solution

Answer

14%

Step 1 - Understand the problem

Find the percentage of the total budget cuts to the Arizona university system that is being cut from the Northern Arizona University budget.

Step 2 - Identify given values

The total budget cuts to the Arizona university system is \[ \$141.5 \text{ million} \]. The amount cut from the Northern Arizona University (NAU) budget is \[ \$20.5 \text{ million} \].

Step 3 - Set up the formula for percentage

To find the percentage, use the formula: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \% \]

Step 4 - Substitute the values into the formula

Plug in the given values into the formula: \[ \text{Percentage} = \left( \frac{20.5 \text{ million}}{141.5 \text{ million}} \right) \times 100 \% \]

Step 5 - Perform the calculation

Calculate the fraction: \[ \frac{20.5}{141.5} \approx 0.1449 \] Multiply this result by 100 to convert it to a percentage: \[ 0.1449 \times 100 = 14.49 \% \]

Step 6 - Round to the nearest percent

Round 14.49% to the nearest whole number: 14%. Hence, 14% of the budget cuts to the Arizona university system is being cut from the Northern Arizona University budget.

Key Concepts

Budget Cuts

Budget cuts refer to reductions in financial allocations. In this case, the Arizona university system faced significant budget reductions. Budget cuts are common in educational institutions, often leading to less funding for programs, staff, and resources. By understanding the percentage calculation of budget cuts, we can assess the impact on specific institutions, like Northern Arizona University (NAU) in this instance.

Percentage Formula

Calculating percentages helps us understand parts of a whole. The formula to find a percentage is: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \% \). In our example, the 'part' is the budget cut from NAU (\$20.5 million), and the 'whole' is the total budget cut from the Arizona university system (\$141.5 million). Using the percentage formula clarifies how much of the total budget cut is attributed to NAU.

Rounding Percentages

Sometimes, percentages are best understood when rounded to a whole number. After calculating a percentage, it's helpful to round to make it easier to interpret. To round a number, look at the digit immediately to the right of your desired decimal place. If it's 5 or higher, round up. If it's lower, round down. In our exercise, we calculated 14.49%, then rounded to 14%.

Elementary Algebra

Elementary algebra involves basic mathematical operations used to solve problems. It includes working with variables and constants. In our example, we used basic algebra to find the percentage of budget cuts. By substituting values into our formula and performing simple calculations, we can use algebra to solve real-world problems. Algebra is essential for understanding and calculating percentages.