Problem 47 - Algebra 1: Concepts and Skills

Question

You want to exchange 60 dollars Canadian dollars into United States dollars. The exchange rate is 1.466 Canadian dollars per United States dollar on the day you exchange the money. How many United States dollars will you get? F. 41 dollars G. 46 dollars H. 131 dollars J. 221 dollars

Step-by-Step Solution

Answer

So, the closest answer to 40.94 dollars is 41 dollars (F).

Step 1: Understand the Conversion Ratio

The exchange rate is given as 1.466 Canadian dollars per United States dollar. This means, for one US dollar, one needs 1.466 Canadian dollars.

Step 2: Apply the Conversion Ratio

To find out how many US dollars one can get with 60 Canadian dollars, divide 60 by the exchange rate 1.466.

Step 3: Calculate the Amount in United States Dollars

Perform the division as in step two, which gives us approximately 40.94 US dollars.

Key Concepts

Exchange Rate

An exchange rate is a key concept in the currency exchange process. It represents the value of one currency in relation to another. For the exercise at hand, the exchange rate tells us how much Canadian dollars (CAD) is equivalent to one United States dollar (USD). The rate given in the exercise is 1.466. This means that 1 USD costs 1.466 CAD.
Understanding this rate is crucial because it dictates how much of a foreign currency you can get with your domestic money. If you want to exchange CAD to USD, knowing the rate allows you to calculate the amount of US dollars you will receive. In this way, the exchange rate acts like a price tag, tagging the cost of one US dollar in terms of Canadian dollars.
In the global financial system, exchange rates fluctuate due to various factors such as economic conditions, market speculation, and political stability. However, for solving textbook problems like the one we have, we take the exchange rate as a fixed value at the time of transaction.

Division

In this exercise, division is the mathematical operation required to convert Canadian dollars into US dollars. Once we understand the exchange rate, the next step is to find out how many US dollars one can obtain with a given amount of Canadian dollars. This is where division comes into play.
To calculate the equivalent US dollar amount, you take the total Canadian dollars you have and divide it by the exchange rate. In mathematical terms, this is represented as:

• Amount in USD = Amount in CAD / Exchange Rate

For example, using the given numbers, we divide 60 CAD by 1.466. This gives us about 40.94 USD. Division is crucial here because it helps break down the problem, allowing us to see how each part of the conversion works according to the exchange rate.

Conversion Ratio

The conversion ratio is essentially another term for the exchange rate, but it highlights a ratio-like perspective of the process. It is the proportional rate used to convert one currency to another; in this case, CAD to USD.
Understanding this as a ratio can make it easier to grasp. Think of it as if for every 1 USD, you must have 1.466 CAD. Thus, the relationship between currencies is determined by this conversion ratio. It serves as a bridge connecting the two different units.
Another advantage of viewing it as a ratio is that it facilitates quick mental conversions. For example, if you know the conversion ratio, you can quickly estimate how much USD you can get from any specific amount of CAD and vice versa.

Canadian Dollar to US Dollar Exchange

When exchanging currencies from Canadian dollars to United States dollars, it's important to understand the practical aspects of the exchange. You need to be aware of the current exchange rate, which acts as your guide. In the exercise, this rate is 1.466.
For the transaction:

• First, check the current exchange rate like in our example.
• Then, prepare to perform the conversion by understanding that you need to use division.
• The amount of Canadian dollars you have is divided by the exchange rate to yield the equivalent in US dollars.

By breaking down the steps and acknowledging the importance of each component—exchange rate, division, and conversion ratio—you ensure the transaction is accurate and efficient. This understanding is vital for various real-world scenarios where currency exchange plays an integral role, such as travel, cross-border shopping, or international finance. Being prepared and knowledgeable about these calculations can help you make smart monetary decisions.