Question

Use 114.520 yen per United States dollar as the rate of currency exchange. You are visiting Japan and have taken $325 to spend on your trip. You have 605 yen left after your trip. How many dollars will you get back?

Short answer

If you exchange the remaining 605 yen to dollars, you will get back approximately $5.28

Step-by-step solution

Calculate total yen

At the beginning of the trip, we had $325. This amount was converted to yen. To find out how much yen that is: \[ 325 \times 114.520 = 37234 \] yen

Calculate yen spent

After the trip, we have 605 yen left. We need to calculate how much yen we spent during the trip, which would be: \[ 37234 - 605 = 36629 \] yen

Convert remaining yen to dollars

We have 605 yen left and we want to convert this back to dollars. We use the given exchange rate of 114.520 yen per dollar to do this: \[ 605 \div 114.520 = 5.28 \] dollars

Key concepts

Algebraic Word Problems

Solving algebraic word problems often involves a few distinct steps: understanding the problem, translating the words into algebraic expressions or equations, solving these equations, and then interpreting the results. In the case of our currency exchange scenario, the problem presents a real-world situation where you need to find out how much money you'll get back after spending a certain amount abroad. Understanding is achieved by reading the problem carefully and determining what you are asked to find and what information is given. This process includes identifying the key components: the initial amount in dollars, the amount spent, and the exchange rate. Then, you must set up an algebraic equation reflecting the situation. In our exercise, this relates to converting dollars to yen and then back to dollars using the given exchange rate. As you work through the steps, each translation from English to algebra gets you closer to the answer.

Unit Rate Conversion

Understanding unit rate conversion is essential for various applications, including currency exchange. A unit rate is a comparative value that expresses the amount of one item in relation to a single unit of another item. In the context of currency conversion, it tells us how much of one currency is equivalent to one unit of another currency. For example, the provided rate of 114.520 yen per United States dollar is a unit rate; it shows the value of 1 US dollar in yen.

Converting currency involves using this unit rate to calculate the worth of a different amount than the standard one unit. Multiplying or dividing by the given unit rate allows you to convert between currencies easily. For exercise improvement advice, it is beneficial to clarify that you multiply the initial amount in dollars by the exchange rate to find the starting yen. Then, by dividing the remaining yen by the exchange rate, you can find the value in dollars once again.

Exchange Rate Calculation

Calculating the exchange rate is a fundamental math skill in the globalized world. An exchange rate is the price at which two currencies can be exchanged against each other. This rate constantly fluctuates due to market conditions, which is why it's important to use the precise rate given at the time of conversion when dealing with word problems or in real life.

To apply the given exchange rate in our exercise, you need to perform two calculations: convert the initial dollar amount to yen and then convert the remaining yen back to dollars at the end of the trip. It's like a two-way conversion process where you first 'buy' yen with your dollars, spend some of them, and then 'sell' the remaining yen to get dollars back. The improvement advice here would emphasize checking whether to multiply or divide during these conversions. To clarify further, when converting to a foreign currency, you multiply by the exchange rate, and when converting back, you divide by the exchange rate.