Problem 3 - Algebra 2

Question

On January \(1,1999,\) the euro became legal tender in 11 participating countries in Europe. Based on the exchange rate on one particular day, the linear function \(d(x)=0.8881 x\) could be used to convert \(x\) euros to U.S. dollars. On that day, what was the value in U.S. dollars of 200 euros?

Step-by-Step Solution

Answer

The value is 177.62 U.S. dollars.

Step 1: Understand the Conversion Function

The function given is \(d(x) = 0.8881x\). This function converts euros (\(x\)) into U.S. dollars by multiplying the amount in euros by the exchange rate, which is 0.8881.

Step 2: Input the Amount in Euros

We need to find the value in U.S. dollars for 200 euros. Here, \(x = 200\). We will substitute this value into the conversion function \(d(x)\).

Step 3: Substitute and Calculate

Substitute 200 for \(x\) in the equation: \(d(200) = 0.8881 \times 200\). Now, perform the multiplication to find the value in U.S. dollars.

Step 4: Perform the Multiplication

Calculate \(0.8881 \times 200\). This results in 177.62, which represents the value in U.S. dollars.

Key Concepts

Currency Conversion

Currency conversion is the process of exchanging one currency for another based on a specific rate.When dealing with money from different countries, it's crucial to convert currency into a more usable form.It's like translating languages. This helps in pricing goods or services overseas, as well as in managing investments.

Imagine you're traveling from Europe to the United States.With money in euros, you'll need U.S. dollars to shop and dine.Each euro you hold has an equivalent value in dollars based on the conversion rate.In the exercise, the conversion function is given as \(d(x)=0.8881x\).This function directly converts any amount in euros, represented as \(x\), into U.S. dollars by applying this rate.Understanding this concept simplifies the process of finding how much your euros are worth in American currency.

Exchange Rate

The exchange rate is a value that tells you how much one currency is worth in terms of another. It's like a bridge that connects different currencies, allowing them to be converted. Exchange rates fluctuate constantly and can vary between banks and currency exchangers.

On the day referenced in the exercise, the exchange rate was 0.8881. This rate means that one euro could be exchanged for approximately 0.8881 U.S. dollars. Therefore, if you had 200 euros, you would compute its dollar equivalent by multiplying the amount by this rate.

Understanding exchange rates is crucial for international trade, tourism, and financial markets. It affects how affordable or expensive goods are when purchased across borders. This means sensitive financial decisions rely on getting the current and most favorable rates.

Algebraic Expressions

Algebraic expressions are mathematical phrases that use numbers, variables, and operations to represent a quantity.In this context, the expression \(d(x) = 0.8881x\) is an example of an algebraic expression and a linear function.

A linear function maps a relationship between two variables in a straight line on a graph.Here, it shows the relationship between euros and U.S. dollars, emphasizing a direct and proportional exchange process.

By substituting a specific value for \(x\), you calculate the desired conversion amount.For instance, inputting 200 for \(x\) in the expression calculates how many U.S. dollars those euros equate to.This linear formula allows for swift calculations without manually handling the exchange rate over and over.It highlights the elegance of algebra in simplifying daily financial tasks.