Question

The U.S. trade deficit at the beginning of 2005 was \(\$ 475,000,000\). If the wealthiest \(1.00\) percent of the U.S. population \((297,000,000)\) contributed an equal amount of money to bring the trade deficit to \(\$ 0\), how many dollars would each person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person living abroad at the time decides to pay in pounds sterling (f). How many pounds sterling does this person contribute (assume a conversion rate of \(1 \mathrm{f}=\$ 1.869) ?\)

Short answer

Each person would need to contribute approximately $159.93. If one person were to pay in nickels only, they would need 3,199 nickels. If another person living abroad wants to make their payment in pounds sterling, they would need approximately 85.49f.

Step-by-step solution

Calculate the amount each person contributes

To find the amount each person in the wealthiest 1.00% of the U.S. population needs to contribute, we can divide the total trade deficit by their population: Number of wealthy people = \(297,000,000 * 1.00\%\) Amount each person contributes = \(\frac{\text{Total Trade Deficit}}{\text{Number of Wealthy People}}\)

Convert the contribution amount into nickels

To find how many nickels are needed, we need to convert the contribution amount into nickels: 1 dollar = 20 nickels Number of nickels = Contribution Amount (in dollars) * 20

Convert the contribution amount into pounds sterling

To find how many pounds sterling they would need to contribute, we can use the given conversion rate: 1 pound sterling = $1.869 Amount in pounds sterling = \(\frac{\text{Contribution Amount (in dollars)}}{\text{Conversion Rate}}\) Now, let's put these steps together by doing the calculations.

Calculations

Step 1: Number of wealthy people = \(297,000,000 * 1.00\% = 2,970,000\) Amount each person contributes = \(\frac{\$475,000,000}{2,970,000} \approx \$159.93\) Step 2: Number of nickels = \(159.93 * 20 \approx 3,198.6\) Since we can't have a part of a nickel, we will round up to the nearest whole number: \(3,199\) Step 3: Amount in pounds sterling = \(\frac{\$159.93}{1.869} \approx 85.49f\) #Answer#: Each person would need to contribute approximately \( \$159.93\). If one person were to pay in nickels only, they would need \(3,199\) nickels. If another person living abroad wants to make their payment in pounds sterling, they would need approximately \(85.49f\).

Key concepts

The Concept of Wealth Distribution

The idea of wealth distribution is crucial in understanding how resources, including money, are allocated across different groups within a society. In this exercise, we explore the situation where the wealthiest 1% of the U.S. population is tasked with eliminating a trade deficit of $475 million.
To break this down:

• First, identify the wealthiest 1% of a total population of 297 million people.
• This would amount to approximately 2.97 million individuals.
• These wealthy participants each need to contribute equally to cover the deficit.

This approach underscores the impact of wealth concentration, where a relatively small group can significantly influence the country's financial obligations through collective contributions. Understanding wealth distribution is a foundation underlying many economic policies and debates.

Understanding Currency Conversion

Currency conversion is the process of changing one form of currency into another to facilitate international financial transactions. In our exercise, one person chooses to pay their share of the trade deficit in pounds sterling rather than dollars.
Let's explore:

• The conversion rate given is 1 pound sterling (f) equals \(1.869.
• We convert the required dollar amount of \)159.93 into pounds sterling using this rate.
• That is calculated as: \(\frac{159.93}{1.869} \approx 85.49f\).

This process is key for individuals and businesses operating across borders, as it ensures they can engage effectively in trade using the applicable currency. Mastering currency conversion helps manage and anticipate financial exchanges accurately in a global economy.

Nickel Conversion Calculations

Nickel conversion refers to translating a specific dollar amount into the equivalent value in nickels. In this example, one individual's contribution of \(159.93 is to be paid entirely in nickels.
Here's how it works:

• Each dollar consists of 20 nickels (since each nickel is 5 cents).
• The person's contribution in dollars is multiplied by 20 to find the total number of nickels needed.
• For \)159.93, the calculation would be: \(159.93 \times 20 = 3,198.6\).
• Since you can't have part of a nickel, round up to 3,199 nickels.

Practical knowledge of such conversions emphasizes the tangible nature of currency and helps one plan for any unusual payment methods required by specific circumstances.

Mathematical Problem-Solving Skills

Mathematical problem-solving is vital for tackling complex scenarios that involve significant calculations or conversions. This exercise is a practical application of these skills.
To solve the problem effectively:

• Identify all the relevant numbers and conversion factors.
• Apply mathematical operations such as division and multiplication to break down the problem into manageable steps.
• Calculate solutions for each section, ensuring accuracy and precision.

Developing these skills not only helps in academic settings but is equally beneficial in everyday situations where logical and quantitative evaluation is necessary. Through exercises like these, students enhance their ability to think critically and resolve real-world mathematical challenges.