Problem 9 - Elementary Algebra

Question

A discount warehouse offers a box of 55 individual instant oatmeal servings for \(\$ 11.10\). The supermarket offers smaller boxes of the same product containing 12 individual servings for \(\$ 3.60 .\) Which store offers the better value?

Step-by-Step Solution

Answer

The discount warehouse offers the better value with a lower unit price.

Step 1: Calculate the Unit Price at Discount Warehouse

To find the unit price at the discount warehouse, divide the total cost of the box by the number of servings. This is calculated as \( \frac{11.10}{55} \).

Step 2: Calculate the Unit Price at Supermarket

To find the unit price at the supermarket, divide the total cost of the box by the number of servings. This is calculated as \( \frac{3.60}{12} \).

Step 3: Comparison of Unit Prices

After calculating the unit prices for both stores, compare the values to determine which is cheaper.

Step 4: Conclusion

The discount warehouse offers the better value as its unit price is lower.

Key Concepts

Discount Warehouse

The concept of a discount warehouse centers around the idea of providing goods in larger quantities at a reduced price per unit. These stores often sell bulk items and larger packaging sizes to pass the savings onto the consumer. The main advantage is the lower unit price, which means you pay less for each individual item when buying a large package compared to smaller, individual purchases.

To understand this, consider a discount warehouse offering a box of 55 instant oatmeal servings for $11.10. Calculating the unit price involves dividing the total cost by the number of servings: \[\text{Unit Price at Discount Warehouse} = \frac{11.10}{55} = 0.202 \text{ dollars per serving}\]Buying in bulk usually results in a better deal per serving or item, provided you can use or store the quantity you purchase. It's a fantastic option for families or those looking to save money over the long term.

Supermarket Comparison

When you analyze supermarket pricing, you're often dealing with smaller packages. These stores are designed more for everyday shopping needs rather than bulk buying. Supermarkets may seem more convenient for short-term needs, but they often have a higher cost per unit.

In our exercise, the supermarket sells a box of 12 servings for $3.60. To find the unit price, we calculate:\[\text{Unit Price at Supermarket} = \frac{3.60}{12} = 0.30 \text{ dollars per serving}\]Supermarket prices can be influenced by convenience factors, competition, and packaging, making the unit cost higher than at discount warehouses. While the upfront cost might seem lower due to smaller sizes, frequent purchasing of these small packages can add up over time.

Value Analysis

Value analysis is key when deciding between buying from a discount warehouse or a supermarket. It's a method of determining the best financial deal by comparing unit prices. Breaking down the total cost into the price per unit offers a clearer picture of which is more economically beneficial.

To perform a value analysis, follow these steps:

• Calculate the unit price for each option by dividing the total price by the number of units.
• Compare the unit prices.
• Choose the option with the lower unit price for better value.

In our example, the unit price comparison between 0.202 dollars per serving at the discount warehouse and 0.30 dollars per serving at the supermarket clearly shows that purchasing from the warehouse provides better value.

Ultimately, the decision also hinges on other factors such as storage capability, cash flow, and personal consumption needs. However, performing a value analysis ensures you make an informed choice.