Problem 65 - Elementary Algebra

Question

At many colleges and universities, students pay tuition and fees, which do not include the costs of room, board, or books. Find the percent of the total amount of tuition and fees that is from fees. Round to the nearest percent. The university is charging a \(\$ 51\) "energy surcharge" for rising electricity costs. A \(\$ 270\) "technology fee" for computer service ... the \(\$ 371.25\) fee for the campus health center, a \(\$ 135\) fee to maintain buildings and grounds and a \(\$ 624\) "incidental fee" for student activities. .. . all told, fees add up to \(\$ 1,542 \ldots\) on top of tuition of \(\$ 3,984\). (Source: www.nytimes .com, Sept. 7, 2007)

Step-by-Step Solution

Answer

The fees account for 28% of the total tuition and fees.

Step 1 - Add Up the Fees

Combine all the fees together: \(51 + 270 + 371.25 + 135 + 624\). The total fees are given as \(1542\), confirming the individual components add up correctly.

Step 2 - Calculate the Total Cost

Add the total tuition cost to the total fees. Therefore, the total cost is: \(3984 + 1542\).

Step 3 - Determine Percentage of Fees

Divide the total fees by the total cost and multiply by 100 to find the percentage: \[\left(\frac{1542}{3984 + 1542} \right) \times 100\].

Step 4 - Perform the Computation

Compute the result: \[\left(\frac{1542}{5526} \right) \times 100 = 27.9\].

Step 5 - Round to the Nearest Percent

Round the result from step 4 to the nearest percent. The answer is \(28\%\).

Key Concepts

percent calculations

Understanding percent calculations is essential in many areas of algebra and real life. Percent means 'out of 100'. To find the percentage of a quantity, you divide the part by the whole, then multiply by 100. For example, if you want to find what percent of a total amount is contributed by a part:

• Divide the part by the whole to get a decimal
• Multiply the decimal by 100 to convert it to a percentage

Let's break it down with a simple example: If you have 20 apples out of a total of 50 fruits:

• Divide 20 by 50 to get 0.4
• Then multiply 0.4 by 100 to get 40%

This same process is used in the exercise to find the percentage of fees out of the total tuition and fees combined.

tuition and fees

Tuition is the money charged by schools and universities for instruction. Fees, on the other hand, are additional charges that cover other costs like libraries, labs, health centers, and activities. Students must pay both tuition and fees, which can add up to a significant amount. In the exercise:

• Tuition is \(3984
• Fees amount to \)1542

These fees include specific items like energy surcharges, technology fees, and incidental fees. To understand the cost structure, you must add all these components separately, then combine them with the tuition to get the total amount.

problem solving steps

In math, breaking down a problem into manageable steps makes it easier to solve. Here's a brief overview of the steps used to solve the given problem:
Step 1: Add up the fees Combine all individual fees to get a total fee amount: \(51 + 270 + 371.25 + 135 + 624 = 1542\)
Step 2: Calculate the total cost Add the tuition to the total fees to get the combined cost: \(3984 + 1542 = 5526\)
Step 3: Determine the percentage of fees Divide total fees by the combined cost and multiply by 100: \left(\frac{1542}{5526}\right) \times 100 = 27.9\
Step 4: Round to the nearest percent Round the result from step 3 to get the final percentage: 28%
By following these steps, you can handle similar percent calculation problems easily.