Question

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches are 2.76 euros per kilogram. Given that there are approximately 1.44 euros to the dollar, calculate what a pound of peaches will cost in dollars.

Short answer

A pound of peaches will cost approximately \(1.80\) dollars.

Step-by-step solution

Convert the cost from euros per kilogram to dollars per kilogram

Given: Cost of peaches in euros per kilogram = 2.76 euros Conversion rate between euros and dollars = 1 euro = 1.44 dollars To convert the cost from euros to dollars, we will multiply the cost of peaches in euros by the conversion rate. Cost of peaches in dollars per kilogram = Cost of peaches in euros per kilogram * Conversion rate Cost of peaches in dollars per kilogram = 2.76 euros * 1.44 dollars/euro = \(3.9744\) dollars/kg

Convert the cost from dollars per kilogram to dollars per pound

Given: Cost of peaches in dollars per kilogram = 3.9744 dollars Conversion between kilograms and pounds = 1 kilogram = 2.20462 pounds To convert the cost from dollars per kilogram to dollars per pound, we will divide the cost in dollars per kilogram by the conversion rate between kilograms and pounds. Cost of peaches in dollars per pound = Cost of peaches in dollars per kilogram / Conversion between kilograms and pounds Cost of peaches in dollars per pound = 3.9744 dollars/kg * (1 kg / 2.20462 pounds) Cost of peaches in dollars per pound = \(1.8031\) dollars/pound Therefore, a pound of peaches will cost approximately 1.80 dollars.

Key concepts

Unit Conversion

Unit conversion is a critical skill in many aspects of life, particularly when dealing with international transactions like purchasing items in a country with a different currency or measurement system. Think of unit conversion as a translation process between two languages, where you're translating the value of one type of unit into the equivalent value in another unit.

Why is Unit Conversion Important?

Understanding how to convert units is essential, not only in math problems but also in real-life scenarios, such as cooking, construction, and especially when traveling. If you can grasp the concept of unit conversion, it can save you from misunderstandings or financial losses in day-to-day transactions.

For example, consider that most countries use the metric system, which includes kilograms for weight, whereas the United States typically uses the imperial system, where weight is measured in pounds. Knowing how to convert between these units can help you make sense of quantities no matter where you are.

Currency Exchange Rate

The currency exchange rate is the value of one currency for the purpose of conversion to another. It is the rate at which you can exchange one country's currency for another. These rates fluctuate constantly due to changes in the global economy, trade, and geopolitical stability, among other factors.

How Does the Currency Exchange Rate Affect Purchases?

When you travel abroad or buy something from a foreign country online, the exchange rate will dictate how much you're actually spending in your own currency. Recognizing this rate allows you to budget properly and avoid unexpected expenses. If you're a student studying currency conversion problems, understanding exchange rates helps in solving mathematical questions related to international buying or selling effectively.

Mathematical Problem-Solving

Mathematical problem-solving involves using mathematical concepts and procedures to find solutions to everyday problems or abstract situations. The process generally includes understanding the problem, devising a plan, implementing the plan, and reflecting on the solution to validate it.

Applying Mathematical Problem-Solving

In the case of our currency conversion problem, mathematical problem-solving is applied by breaking down the task into manageable steps. The first step might be converting euros to dollars, which requires understanding exchange rates. The next step is to address unit conversion, turning kilograms into pounds in this instance. By clearly understanding each component and its application, problem-solving becomes a series of logical and manageable steps on the way to finding the correct answer.