Question

In continental Europe, one "pound" is half a kilogram. Which is the better buy: one Paris pound of coffee for $$\$ 9.00$$ or one New York pound of coffee for $$\$ 7.20 ?$$

Short answer

Given the cost per kilogram calculated, the New York coffee at around $15.86 per kilogram is a better buy than the Paris coffee at $18 per kilogram.

Step-by-step solution

Convert the weights to a common unit

Begin by understanding that a pound in Europe (Paris pound) is half a kilogram, while a pound in New York is typically about 0.454 kilogram. Therefore, convert these weights to a common unit which is kilogram. So we have, 1 Paris pound = 0.5 kg and 1 New York pound = 0.454 kg.

Calculate the cost per kilogram for each type of coffee

Determine the cost per kilogram for each type of coffee. This can be done by dividing the price of each pound by its weight in kilogram. For the Paris coffee, this is \(\$9 / 0.5kg\), resulting in a cost per kilogram of \(\$18/kg\). For the New York coffee, this is \(\$7.20 / 0.454kg\), resulting in a cost per kilogram of about \(\$15.86/kg\).

Compare the cost per kilogram of Paris coffee with New York coffee

Now that the cost per kilogram for each type of coffee is known, compare the two. Among the options, the coffee with the lowest cost per kilogram will be the better buy.

Key concepts

Cost Analysis

Cost analysis is an essential tool when deciding between different purchasing options. It involves comparing different factors such as price, weight, and quality to find the most economical choice. In our coffee example, we analyze the cost per kilogram to determine which is the better buy.

Here’s how to approach it:

• Calculate the actual cost per unit (in this case, per kilogram) for each option.
• Compare these costs to determine which option offers the best value for money.

For the coffee samples, the Paris pound's price is calculated by dividing the price by the weight: \[\frac{9}{0.5} = 18 \, \text{dollars/kilogram} \]Similarly, for the New York pound: \[\frac{7.20}{0.454} \approx 15.86 \, \text{dollars/kilogram} \]Choose the lower cost, indicating which is more economical.

Metric System

The metric system is a decimal-based system of measurement used worldwide, and it simplifies calculations by using units that are easily divisible by ten. When dealing with international comparisons, like comparing French and American weights, using this system makes things clearer.

For example:

• In Europe, a pound refers to half a kilogram.
• In the US, a pound means approximately 0.454 kilograms.

To compare effectively, it is important to convert both weights to the metric system, thus using kilograms. This conversion ensures that you're comparing 'apples to apples.' For the exercise, we converted the Paris pound to 0.5 kg and the New York pound to 0.454 kg. This harmonization using the metric system allows for a more precise comparison.

Weight Comparison

Weight comparison is vital when prices are linked directly to weight, as seen with coffee. We started with understanding that different regions use different meanings for the term 'pound.' Recognizing these differences enables us to compare products accurately.

Key steps include:

• Identifying the exact weight of the items being compared (ie: 0.5 kg in Paris, 0.454 kg in New York).
• Using a common weight measurement (kilograms) for both to standardize the comparison.

Since the Paris pound is greater than the New York pound, converting these units helps in calculating the cost per kilogram accurately. By ensuring fair comparison, it makes conclusions about value for money clear.