Problem 48 - Prealgebra

Question

Explain how equations are used to find the U.S. value of foreign currency. Illustrate your reasoning by finding the cost in U.S. dollars of a 12 -pound bus trip in Egypt, if 6 pounds can be exchanged for one U.S. dollar.

Step-by-Step Solution

Answer

The 12-pound bus trip costs 2 U.S. dollars.

Step 1: Understanding the Problem

We need to find the cost in U.S. dollars for a bus trip that costs 12 pounds, with the exchange rate of 6 pounds to 1 U.S. dollar. This involves currency conversion, which can be approached using equations.

Step 2: Setting Up the Equation

To find the U.S. dollar value, set up the equation where 12 pounds is converted to dollars using the exchange rate. The equation will be: \[\text{Cost in Dollars} = \frac{\text{Cost in Pounds}}{\text{Exchange Rate (Pounds per Dollar)}}\] Substitute the given values: \[\text{Cost in Dollars} = \frac{12}{6}\]

Step 3: Solving the Equation

Divide 12 (the cost in pounds) by 6 (the exchange rate for pounds per dollar): \[\text{Cost in Dollars} = 2\]This means that the cost of the bus trip in U.S. dollars is 2.

Step 4: Conclusion

Equations help convert foreign currency to U.S. dollars by dividing the total foreign currency by the exchange rate. Here, we used the equation to convert 12 pounds to 2 dollars given the exchange rate of 6 pounds per dollar.

Key Concepts

Understanding Exchange Rates

Exchange rates tell us how much one currency is worth when compared to another. In our exercise, we are looking at the exchange rate between pounds and U.S. dollars. Specifically, 6 pounds can be exchanged for 1 U.S. dollar. This rate is like a bridge that connects two different systems of currency. If you have pounds and need dollars, you must know this rate to make the conversion.

Exchange rates can fluctuate based on economic factors such as inflation, interest rates, and geopolitical events. For this exercise, the exchange rate is fixed at 6 pounds per dollar. It's essential to understand this rate, as it will guide your calculations for converting currency.

Using Equations in Prealgebra

To solve problems involving exchange rates, prealgebraic equations are a handy tool. They allow you to model the conversion process mathematically. In this scenario, we have posed an equation to determine how many dollars 12 pounds equals, using the given exchange rate.

The equation used is: \[\text{Cost in Dollars} = \frac{\text{Cost in Pounds}}{\text{Exchange Rate (Pounds per Dollar)}}\]By substituting the known values into this equation, you can calculate the equivalent dollars. This equation is a straightforward way to express and solve the currency conversion problem, ensuring clarity and accuracy in calculating the required amount in U.S. dollars.

Problem-Solving Steps

Solving currency conversion problems with equations involves several clear steps. These steps ensure you are using the right information and procedures to arrive at the correct solution.

• First, understand the problem: Recognize that you need to convert a foreign currency amount to its U.S. dollar equivalent.
• Second, identify the exchange rate given (6 pounds per 1 U.S. dollar in this case).
• Third, set up your equation, placing the foreign currency value in the numerator and the exchange rate as the divisor.
• Finally, perform the division to solve the equation, providing you with the currency value in dollars.

Following these clear and methodical steps aids in avoiding errors and ensures that the final solution reflects accurate currency conversion.