Problem 30 - Elementary Algebra

Question

If \(8 \%\) of the receipts of a sporting event are donated to charity and the receipts total \(\$ 48,000\), find the amount donated to charity.

Step-by-Step Solution

Answer

\$ 3,840

Step 1 - Understand the percentage

Recognize that 8% means 8 out of every 100 units. In this case, it means 8% of the total receipts will go to charity.

Step 2 - Convert percentage to a decimal

Convert 8% to a decimal by dividing by 100: \[ 8\text{%} = \frac{8}{100} = 0.08 \]

Step 3 - Calculate the donated amount

Multiply the total receipts by the decimal value to find the donation amount: \[ \text{Donation Amount} = 48000 \times 0.08 = 3840 \]

Key Concepts

converting percentages to decimals

Converting percentages to decimals is a crucial skill when it comes to percentage calculations. Percentages represent parts per hundred, so converting them involves dividing by 100. For example, to convert 8% to a decimal, divide 8 by 100:
\[\frac{8}{100} = 0.08\]
This means that 8% is the same as 0.08 in decimal form. Understanding this conversion can simplify many math problems.

multiplication

Once we have converted the percentage to a decimal, the next step usually involves multiplication. Multiplication lets us find a part of a whole by multiplying the whole by the decimal. In our example, we have \$48,000\$ in total receipts, and we need to find out how much is 8% of it. Multiply 48000 by 0.08 to get the donation amount:
\[\text{Donation Amount} = 48000 \times 0.08 = 3840\]
Hence, the amount donated to charity is \$3,840\$. This process is straightforward and can be used in various scenarios involving percentages.

real-world applications

Understanding how to calculate percentages and apply them in real-world situations is a valuable skill. In our scenario, we calculated the donation amount from a sporting event. Such calculations are common in various fields:

• Finance: Finding interest rates and discounts
• Health: Calculating medication dosages
• Shopping: Determining sale prices

Mastering percentage calculations can help you make informed decisions and understand everyday transactions better. Whether you're organizing an event, managing finances, or even just shopping, knowing how to work with percentages ensures accuracy and confidence.