Problem 58 - Chemistry: An Atoms-Focused Approach

Question

The price of a popular soft drink is \(\$ 1.00\) for 24 fluid ounces \((\mathrm{fl} \text { oz })\) or \(\$ 0.75\) for \(0.50 \mathrm{L}\). Which is a better buy? \((1 \mathrm{qt}=32 \mathrm{floz})\)

Step-by-Step Solution

Answer

Answer: The 24 fluid ounce drink for $1.00 is the better buy.

Step 1: Convert volume measurements to a single unit

It is important to have all volume measurements in one unit, so let's convert 0.50L to fluid ounces. We are given that \(1\,qt=32\,floz\). We can also use the conversion factor, 1 liter = 33.814 fluid ounces. Therefore, we can convert 0.50 liters to fluid ounces: \(0.50\,L \times \frac{33.814\,floz}{1\,L} = 16.907\,floz\) Now we have the volumes for both options in fluid ounces: 24 fluid ounces for the first option, and approximately 16.907 fluid ounces for the second option.

Step 2: Calculate the price per fluid ounce for both options

In this step, we will find the price per fluid ounce for both options: Option 1: Price = \(\$1.00\) for 24 floz. Price per fluid ounce = \(\frac{\$1.00}{24\,floz} = \$0.0417\,per\,floz\) Option 2: Price = \(\$0.75\) for 16.907 floz. Price per fluid ounce = \(\frac{\$0.75}{16.907\,floz} = \$0.0443\,per\,floz\)

Step 3: Compare the prices

Now that we have the price per fluid ounce for both options, we can compare them: Option 1 price per floz: \(\$0.0417\) Option 2 price per floz: \(\$0.0443\) Since \(\$0.0417 < \$0.0443\) per floz, buying the 24 fluid ounces option for \(\$1.00\) is a better buy.

Key Concepts

Price Comparison

When it comes to shopping, one of the smartest strategies is comparing the unit prices of different options. This helps in identifying the best value for your money. In the world of beverages, specifically soft drinks, this technique can save you a decent amount over time.
To accurately perform a price comparison, always ensure that the quantities are consistent, meaning they should be measured in the same unit. This not only simplifies the comparison process but makes it more reliable.
After converting units, as in our exercise, divide the total price by the quantity to find the price per unit. In our specific exercise, the price per fluid ounce was calculated for two options, allowing us to look at them side by side. The lower the price per unit, the better the deal.

Fluid Ounces Measurement

Fluid ounces (abbreviated as fl oz) are a standard unit of volume in the United States. This measure is commonly used for liquids and is an essential part of grocery shopping. You will find it on labels of bottled drinks, milk cartons, and even cleaning supplies.
Knowing how to measure and understand fluid ounces can help you make informed purchasing decisions. This unit allows us to directly compare different liquid volumes across various products, maintaining consistency. For instance, when comparing drinks, having both measured in fluid ounces gives a clear picture of the quantity each option offers.
Don't confuse fluid ounces with ounces, as the latter is for weight, not volume. This distinction is crucial when you're looking at the nutrition content or pricing of food and drinks.

Liter to Fluid Ounces Conversion

Converting liters to fluid ounces is a handy skill, especially since both units are widely used. In the U.S., everyday liquid consumption is often measured in fluid ounces, while many bottles and packages might display measurements in liters, especially imported ones.
To convert liters to fluid ounces, you can use the conversion factor where 1 liter equals roughly 33.814 fluid ounces. This simple multiplier enables you to switch between the units easily. For example, in our exercise, we converted 0.50 liters to approximately 16.907 fluid ounces by multiplying 0.50 by 33.814.
Having the ability to perform this conversion encourages better shopping practice by allowing straightforward comparisons between products labeled in different units. It provides flexibility and ensures that your purchasing decisions are based on comparable data.