Problem 27 - Prealgebra

Question

Use the following information. In a recent year, 1 U.S. dollar could be exchanged for 0.78 euros. The table shows the relationship between U.S. dollars and euros. $$\begin{array}{|c|c|}\hline \text { U.S. Dollars \(d\) } & \text { Euros \(c\) } \\\\\hline 1 & 0.78 \\ \hline 2 & 1.56 \\\\\hline 3 & 2.34 \\\\\hline 5 & 3.90 \\\\\hline\end{array}$$ How many U.S. dollars can you receive for 7.8 euros?

Step-by-Step Solution

Answer

You can receive 10 U.S. dollars for 7.8 euros.

Step 1: Understand the Conversion Rate

We know from the problem statement that 1 U.S. dollar is equivalent to 0.78 euros. This means for every dollar, we receive 0.78 euros.

Step 2: Set Up the Mathematical Relationship

To find out how many dollars you can get for a given number of euros, we need to rearrange the conversion rate equation. The formula for converting euros to dollars is: \[ d = \frac{c}{0.78} \]where \(d\) is the number of dollars, and \(c\) is the number of euros.

Step 3: Plug in the Given Values

We are asked to find out how many dollars we can get for 7.8 euros. Using the formula:\[ d = \frac{7.8}{0.78} \]

Step 4: Perform the Calculation

Divide 7.8 by 0.78 to find the number of U.S. dollars:\[ d = \frac{7.8}{0.78} = 10 \]

Step 5: Verify the Calculation

Double-check the calculation to ensure it is correct. Re-performing the division confirms that 7.8 euros is indeed equivalent to 10 U.S. dollars.

Key Concepts

U.S. Dollars

The U.S. Dollar, symbolized as USD, is the official currency of the United States of America. It is one of the most widely used currencies in the world, often utilized in international transactions and considered a global currency benchmark. This means many countries use it as a reference or even adopt it as their own currency in certain cases.
When talking about currency conversion, it is crucial to understand the base currency (in this case, the U.S. Dollar) and how much of the foreign currency corresponds to one unit of the base currency. For example, if you have 1 U.S. Dollar, you can convert this into another currency, such as Euros, based on the current exchange rate.

Euros

The Euro, symbolized as EUR, is the official currency of the Eurozone, which consists of 19 of the 27 European Union member countries. It is the second most traded and held currency in the world after the U.S. Dollar, making it a significant player in global financial markets.
The relationship between Euros and U.S. Dollars is defined by the exchange rate. In the given scenario, 1 U.S. Dollar was equivalent to 0.78 Euros. This means that if you have 1 USD in your pocket, you could exchange it for 0.78 EUR at that conversion rate. Understanding how these two currencies interact is essential for anyone dealing with international financial transactions.

Exchange Rate

An exchange rate is the value of one currency for the purpose of conversion to another. It can fluctuate based on economic factors, including inflation, interest rates, and political stability. In our example, the exchange rate is set at 1 U.S. Dollar to 0.78 Euros.
Exchange rates are crucial for businesses, travelers, and investors who need to convert money between different currencies. For individuals, knowing the current exchange rate can help in planning travel expenses or investments abroad. It provides a mathematical way to understand how much one country’s currency is worth compared to another.

Mathematical Relationship

In mathematics, a relationship is a connection between two or more numbers. For currency conversion, the mathematical relationship helps us determine how much one currency is worth in terms of another. The given problem uses this relationship to solve how many U.S. Dollars you get for 7.8 Euros.
We use a formula to establish this relationship:

• The formula is: \[ d = \frac{c}{0.78} \]
• Where \(d\) represents dollars and \(c\) stands for euros.

By plugging the values into the formula, we calculate the equivalent amount in U.S. Dollars. In this example, by dividing 7.8 by 0.78, we get 10. This calculation confirms that 7.8 Euros can convert to 10 U.S. Dollars, showcasing the mathematical precision needed for accurate currency conversion.