Problem 65 - Elementary Algebra Within Reach

Question

Determine which product has the lower unit price. (a) A 2 liter bottle (67.6 ounces) of soft drink for \(\$ 1.09\) (b) Six 12 -ounce cans of soft drink for \(\$ 1.69\)

Step-by-Step Solution

Answer

The 2 liter (67.6 oz) bottle of soft drink for \$1.09 has the lower unit price.

Step 1: Convert the measurements into the same unit

Firstly, take note of the volume specified in each option. Since 1 liter is equivalent to about 33.8 ounces, you should convert the 2 liter in option (a) to ounces by multiplying 2 liters with 33.8 ounces. 2 liters = 2 * 33.8 = 67.6 ounces. Thus, both measurements are now in ounces.

Step 2: Calculate the unit price for each product

The unit price is calculated by dividing the total price of the product by the total amount of the product. For option (a), unit price = \$1.09 / 67.6 ounces = \$0.016 per ounce. For option (b), the total ounces of drink for six 12 ounce cans are 6*12 = 72 ounces. So, unit price = \$1.69 / 72 ounces = \$0.023 per ounce.

Step 3: Compare the unit prices

The unit price for option (a) is \$0.016 per ounce. The unit price for option (b) is \$0.023 per ounce. Since \$ 0.016 is less than \$ 0.023, option (a) has the lower unit price.

Key Concepts

Conversion of Measurements

To compare products effectively, it is crucial to convert all measurements into the same unit. This process helps prevent misunderstandings and allows for accurate comparisons. In this exercise, one option is given in liters and the other in ounces. Since the majority of drink measurements in this problem are in ounces, it's efficient to convert liters into ounces.

For conversion, remember the essential equivalence: 1 liter equals approximately 33.8 ounces. This small conversion factor will help you adjust the liquid volume to the correct unit quickly. To convert, multiply the number of liters by 33.8. For example, a 2-liter bottle can be converted as follows: 2 liters \( \times \) 33.8 ounces per liter = 67.6 ounces. This ensures everything is measured in ounces, making further calculations simpler.

Comparison of Prices

Once conversion is completed, it’s time to compare prices using a standardized measure—unit price. The unit price enables you to see the cost per single unit of product, providing insight into which product offers better value for money.

In this scenario, both products have been converted into the same volume unit, ounces. This makes it straightforward to calculate the unit price. By dividing the total price by the total volume, you obtain the dollar cost per ounce. Doing this for both available options reveals their true value independent of size or packaging differences. Comparing these unit prices (

• option (a): \( \\(0.016 \) per ounce
• option (b): \( \\)0.023 \) per ounce

) shows that option (a) is the cheaper choice per ounce. Remember, finding the cheaper unit price saves money over time.

Basic Arithmetic Operations

Calculating unit price requires a few basic arithmetic operations like multiplication and division. These operations may seem simple, but they are powerful tools in real-world applications.

Firstly, multiplication was used when converting the bottle's volume from liters to ounces by multiplying the number of liters by the ounce conversion factor, 33.8. This is essential for aligning your measurements.

Next comes division, where you take the total cost and divide it by the total ounces. This step gives you the unit cost, allowing for further comparison between options. For instance, calculating the unit price for option (a) involves dividing \( \\(1.09 \) by 67.6 ounces, and for option (b), dividing \( \\)1.69 \) by 72 ounces. Utilizing these basic operations effectively helps in making informed purchasing decisions, reinforcing the value of fundamental math skills in everyday life.