Question

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost \(2.45\) euros per kilogram. Given that 1 euro is equivalent to approximately \(\$ 1.32\), calculate what a pound of peaches will cost in dollars.

Short answer

The cost of a pound of peaches in dollars is approximately \$1.47.

Step-by-step solution

Convert the cost of peaches from euros to dollars

To convert the cost from euros to dollars, we can multiply the cost per kilogram by the exchange rate. We are given the exchange rate to be \(1 Euro \approx \$1.32\): \[2.45 Euros * 1.32 \frac{Dollars}{Euro}\]

Perform the multiplication

Now, we need to multiply the values to find the cost of the peaches in dollars per kilogram: \[Cost = 2.45 * 1.32\] \[Cost \approx \$3.234\]

Convert the weight from kilograms to pounds

To convert the weight of peaches from kilograms to pounds, we need to use the following conversion factor: \(1 kilogram \approx 2.20462 pounds\). First, we need to find the cost per pound: \[\frac{\$3.234}{1 kilogram} * \frac{1 kilogram}{2.20462 pounds}\]

Perform the multiplication and division

Next, we perform the multiplication and the divisions to find the cost per pound: \[Cost = \frac{3.234}{2.20462}\] \[Cost \approx \$1.466\]

Round the result to 2 decimal places

Finally, we round the obtained value to 2 decimal places: \[Cost \approx \$1.47\] So, a pound of peaches will cost about $1.47 in dollars.

Key concepts

Exchange Rate Calculation

Understanding how to calculate exchange rates is a fundamental skill in both traveling and international economics. Exchange rates tell us how much one currency is worth in terms of another. For example, when you hear that 1 euro is equivalent to approximately \(1.32, it means for every 1 euro, you can exchange it for \)1.32. To convert prices from one currency to another, like in our peach buying scenario, you simply multiply the cost by the exchange rate. It's crucial to ensure that the units cancel out properly, leaving you with the desired currency—dollars, in this case. When doing this:

• Always check for the most recent exchange rates, as they can fluctuate.
• Be aware of potential transaction fees that could alter the effective rate you're using in real-life scenarios.
• Remeber that rounding is often necessary when dealing with currency to maintain the practicality of the exchange.

In trading and finance, this calculation helps with budgeting and cost planning when buying goods abroad or engaging in foreign trade. The exercise provided shows a simple multiplication step, converting the cost of peaches from euros to dollars using the given exchange rate.

Metric to Imperial Conversion

Shifting between metric and imperial units is a common hurdle in Chemistry and everyday tasks. The metric system is widely used around the world and is based on units of ten—making conversion between metric units quite straightforward. However, the imperial system—prevalent in the United States—uses units like pounds and ounces, which don't scale as neatly.
For instance, in our exercise, we're taking the price of peaches from a metric weight (kilograms) to an imperial weight (pounds). Conversion factors like '1 kilogram is approximately equal to 2.20462 pounds' are essential. To convert, you divide by this conversion factor if going from metric to imperial or multiply if doing the reverse:

• Always double-check the conversion factors as some might be approximations.
• Keep track of significant figures, as precision is key in scientific and quantitative fields.
• Consider using conversion tables or online calculators to save time and reduce error.

This skill is not only valuable for shopping in foreign countries but also in laboratories, cooking, and industries that involve international shipping and manufacturing.

Quantitative Problem Solving

Quantitative problem solving is a critical thinking process that involves the use of numbers, units, and logical steps to solve real-world problems. It's a pillar of scientific inquiry and mathematical reasoning used across multiple disciplines. The technique requires identifying the given data, determining what needs to be found, and methodically applying operations like addition, multiplication, division, or more complex formulae to arrive at a solution. Key elements include:

• Clearly defining variables and what they represent.
• Maintaining consistent units throughout your calculation.
• Checking that your final units match the desired outcome.
• Rounding the solution appropriately for the context.

In the peach cost problem from our example, we sequentially performed operations—currency conversion followed by unit conversion—to determine the final cost per pound in dollars. This process exemplified quantitative problem solving in a practical context, combining mathematical skills with real-world knowledge to reach an answer that's both accurate and useful.