Question

If \(\$ 1.00\) is equivalent to 1.74 German marks, what is \$20.00 worth in marks? What is the value in dollars of a 100-mark bill?

Short answer

The value of $20.00 in German marks is \(20.00 \times 1.74 = 34.8\) marks. The value of a 100-mark bill in dollars is \(\frac{100}{1.74} \approx 57.47\) dollars.

Step-by-step solution

Calculate the value of $20.00 in German marks

To find the value of \(20.00 in German marks, we will multiply the given conversion rate (1.74 marks per dollar) by \)20.00. \(Value\_in\_marks = Dollars \times Conversion\_rate\) \(Value\_in\_marks = 20.00 \times 1.74\) Calculate the above expression.

Calculate the value of a 100-mark bill in dollars

To find the value of a 100-mark bill in dollars, we will divide the given amount in marks (100) by the given conversion rate (1.74 marks per dollar). \(Value\_in\_dollars = \frac{Marks}{Conversion\_rate}\) \(Value\_in\_dollars = \frac{100}{1.74}\) Calculate the above expression.

Key concepts

Exchange Rate

Understanding the concept of an exchange rate is crucial when dealing with currency conversions. An exchange rate simply tells you how much one country's currency is worth in terms of another currency.
In our example, an exchange rate of 1.74 means that $1.00 is equivalent to 1.74 German marks. This rate acts as a bridge between two currencies, allowing you to translate amounts from dollars to marks, or vice versa.
Exchange rates fluctuate based on economic factors, such as inflation, interest rates, and the overall economic stability of a country. This means that the value of one currency in relation to another can change over time. Keeping this in mind helps to understand why it's important to have the most current exchange rate when making conversions.

Multiplication in Conversions

When converting currency, multiplication is a common operation when you want to exchange your own currency for a foreign currency. In our problem, we multiplied by the exchange rate to find the equivalent amount in German marks.
Here's how to think about it:

• Identify the amount you have in your currency (in this case, \(20.00).
• Use the exchange rate as a unit rate. Here, each dollar is worth 1.74 marks.
• Multiply the amount in your currency by the exchange rate. This gives you the value in the foreign currency.

The formula we used is: \( \text{Value\_in\_marks} = \text{Dollars} \times \text{Conversion\_rate} \). In this example, the calculation would be: \( 20.00 \times 1.74 = 34.80 \), so \)20.00 is equivalent to 34.80 marks.
Using multiplication in this way is straightforward and allows you to directly find how much your currency is worth in another currency.

Division in Conversions

Division comes into play when you want to convert a foreign currency back into your own currency. In the exercise we have, we converted German marks into dollars. For this, we use division.
The process involves:

• Identifying the amount in the foreign currency (100 marks in our case).
• Using the exchange rate to find how many units of your currency are needed per unit of the foreign currency.
• Dividing the amount in the foreign currency by the exchange rate.

The formula is: \( \text{Value\_in\_dollars} = \frac{\text{Marks}}{\text{Conversion\_rate}} \). For our example, this becomes: \( \frac{100}{1.74} \approx 57.47 \), meaning that 100 marks is roughly equivalent to $57.47.
By dividing, you break down the foreign currency amount into equivalent pieces of the home currency, using each part of the foreign currency as defined by the unit rate (exchange rate).
Always remember to use the most current exchange rate to ensure accurate conversions.