Question

Translate to an equation and solve. The 2011 federal budget has \(\$ 0.9\) trillion allocated for the Department of Health and Human Services. If the total budget was \(\$ 3.8\) trillion, what percent of the total budget went toward the Department of Health and Human Services? (Source: Budget of the United States Government, Fiscal Year 2011 .)

Short answer

Question: What percentage of the total budget went toward the Department of Health and Human Services if the allocated budget for the department is $0.9 trillion, and the total budget is $3.8 trillion. Answer: Approximately 23.68% of the total budget went toward the Department of Health and Human Services.

Step-by-step solution

Identify the given values

In this problem, we are given the allocated budget for the Department of Health and Human Services, which is \(\$0.9\) trillion, and the total budget, which is \(\$3.8\) trillion.

Set up the equation

We need to find the percentage of the total budget that went toward the Department of Health and Human Services. The formula for finding the percentage of a part in relation to the whole is: Percentage = \(\frac{Part}{Whole} \times 100\) We can use this formula to create an equation with the given values: Percentage = \(\frac{\$0.9 \,\text{trillion}}{\$3.8 \,\text{trillion}} \times 100\)

Solve the equation

Now we can solve the equation to find the percentage of the total budget allocated for the Department of Health and Human Services: Percentage = \(\frac{\$0.9}{\$3.8} \times 100\) Percentage = \(0.2368 \times 100\) (rounded to four decimal places) Percentage = \(23.68\)

State the answer

Therefore, approximately \(23.68 \%\) of the total budget went toward the Department of Health and Human Services.

Key concepts

Understanding Equations

Equations are powerful mathematical tools that help us express relationships between different quantities. In the context of budgeting, equations allow us to calculate percentages, ratios, and comparisons in a structured way.
In the provided exercise, we used the equation for calculating the percentage to understand how much of the total budget was allocated to a specific department. This particular equation:

• divides the part of the budget allocated to the Department of Health and Human Services ( $0.9 time)$ trillion) by the total budget ( $3.8 time)$ trillion),
• then multiplies the result by $100 time)throws) to convert it into a percentage.

By setting up and solving this equation, students can easily find out what portion of a budget is designated for a specific purpose.

Explaining Budget Allocation

Budget allocation involves distributing financial resources across various sectors or departments to ensure that all necessary operations are funded appropriately. Each segment of a budget is usually a reflection of the organization or government priorities and the anticipated needs.
In the scenario provided, we see how the Department of Health and Human Services was allocated $0.9 time)$ trillion from the total budget of $3.8 ime)$ trillion.
This kind of allocation often considers factors like the previous year’s expenditure, current operational needs, and future planning goals. Analyzing budget allocation can help us understand where emphasis is placed and can provide insights into possible fiscal policy priorities.

Problem Solving with Percentages

When confronted with financial data, it’s common to determine what percentage one amount is of another, especially when analyzing budgets or financial plans. Solving percentage-based problems involves translating real-world scenarios into mathematical expressions or equations.
In problem-solving with percentages, it’s crucial to:

• Identify the 'part' and the 'whole' from the scenario.
• Use the percentage formula as a guide: \(\frac{Part}{Whole} \times 100\\).
• Perform accurate calculations, considering units such as trillions or billions in financial contexts.

Here, understanding the percentage of the total budget allocated can help stakeholders make informed decisions, evaluate current budget allocations, and plan better for future financial requirements.