Problem 61 - Introductory and Intermediate Algebra for College Students 4th

Question

A charity has raised \(\$ 7500\), with a goal of raising \(\$ 60,000\). What percent of the goal has been raised?

Step-by-Step Solution

Answer

The charity has thus far raised 12.5% of their goal.

Step 1: Understand the Problem

We need to find out what percent of the goal of 60000 dollars has been raised. The charity has so far raised 7500 dollars.

Step 2: Set Up the Formula for Percentage

The formula to calculate the percentage is \(\frac{{Part}}{{Whole}} \times 100\%. We will replace 'Part' with 7500 and 'Whole' with 60000.

Step 3: Plug in the Values into the Formula

We replace 'Part' with 7500 and 'Whole' with 60000 in the percentage formula and calculate the result: \(\frac{{7500}}{{60000}} \times 100%\).

Step 4: Calculate the Percentage

After plugging in the values, we calculate the percentage. This yields 12.5%

Key Concepts

Fundraising Goal

A fundraising goal is the target amount a group or organization aims to gather through donations or other means. This is common among charities, non-profit organizations, and even certain businesses. In our example, the charity's fundraising goal is set at \(\$60,000\). It represents the entire sum needed to achieve a specific purpose, such as funding a project or supporting a cause.

Setting a clear fundraising goal is crucial. It helps define strategies and measures the progress of the fundraising efforts. Additionally, knowing the goal provides motivation for the team involved in the fundraising activities.

• A clear target encourages complete effort from all contributors.
• Donors are often more inclined to give if they know how much is needed.
• Tracking progress becomes easier and more tangible when working towards a defined goal.

Reaching the goal not only signifies success but can also amplify future opportunities for the organization to engage more supporters.

Algebraic Expressions

Algebraic expressions are mathematical phrases that include numbers, variables, and arithmetic operations. They do not have an equality sign. In this exercise, the focus is on forming a formula to calculate percentages.

The formula used, \(\frac{\text{Part}}{\text{Whole}} \times 100\%\), is a simple algebraic expression tailored for percentage calculation. Here, "Part" represents the portion already achieved, which is \(\\(7500\), and "Whole" is the total amount needed, \(\\)60,000\). You substitute the known values into the expression to find the percentage of the goal achieved.

• Understand the role of each component in the expression.
• Ensure correct substitution of values to prevent errors.
• A correct algebraic setup is essential for accurate calculations.

Mastering algebraic expressions is foundational for advanced mathematical concepts, making it a valuable skill in various areas of study and real-life applications.

Basic Arithmetic

Basic arithmetic includes the fundamental operations of mathematics: addition, subtraction, multiplication, and division. In this exercise, these operations are central to solving the problem.

After setting up the algebraic formula, the main arithmetic operation involved is division and multiplication. Initially, you divide \(7500\) by \(60000\) to determine the fractional part of the goal reached. The result is then multiplied by \(100\) to convert the fraction into a percentage. Understanding how to execute each operation accurately is key to finding the correct solution.

• Division is used to compare parts of a whole.
• Multiplication adjusts the fraction to a percentage scale.
• Precision in arithmetic ensures accuracy in your final answers.

Basic arithmetic is the backbone of mathematics and a crucial part of daily life activities, from simple budgeting to complex problem-solving scenarios.