Problem 29 - Prealgebra

Question

Which costs more per issue, an 18 -issue subscription for \(\$ 40.50\) or a 12 -issue subscription for \(\$ 33.60 ?\) Explain.

Step-by-Step Solution

Answer

The 12-issue subscription costs more per issue at \( \$2.80 \).

Step 1: Determine the Cost per Issue for the 18-Issue Subscription

To find out the cost per issue for the 18-issue subscription, divide the total subscription cost by the number of issues. Calculate: \( \frac{40.50}{18} \approx 2.25 \). This means each issue costs approximately \( \$2.25 \).

Step 2: Determine the Cost per Issue for the 12-Issue Subscription

Next, calculate the cost per issue for the 12-issue subscription. Divide the total cost by the number of issues: \( \frac{33.60}{12} = 2.80 \). Each issue costs \( \$2.80 \).

Step 3: Compare the Costs

Compare the cost per issue between the two subscriptions. The 18-issue subscription costs \( \\(2.25 \) per issue, while the 12-issue subscription costs \( \\)2.80 \) per issue.

Key Concepts

Understanding Subscription Cost

When you subscribe to a magazine, you usually pay upfront for multiple issues. This upfront payment is called the subscription cost. It's the total sum you pay at once to receive a pre-determined number of issues. Consider a scenario where you subscribe to a magazine delivering 18 issues for \\(40.50, and another with 12 issues for \\)33.60. Here, \\(40.50 and \\)33.60 represent the total subscription costs.

Subscription costs can differ based on the number of issues you'll receive and potential discounts. The higher the number of issues, the potential for a lower price per issue depending on the subscription model. To ensure you're getting the best deal, it's wise to look beyond just the total cost and carefully consider the cost per individual issue as well.

Calculating Price Per Issue

The price per issue provides a clearer understanding of a subscription's value. It's calculated by dividing the total subscription cost by the number of issues. This tells you exactly how much you are paying for each magazine copy.

• For the 18-issue subscription, you divide \\(40.50 by 18, leading to an approximate price per issue of \\)2.25.
• With the 12-issue subscription, splitting \\(33.60 by 12 results in a price per issue of \\)2.80.

Understanding the price per issue is crucial for making informed decisions, especially when comparing multiple subscription offers. This simple calculation shows that, although the 12-issue subscription seems cheaper overall, each individual magazine costs more than the 18-issue subscription.

Essential Mathematical Operations

Mathematical operations are key to finding out which subscription is truly the better deal. Here, we're utilizing basic division to reach an understanding of cost per issue. Division is the process of seeing how many times one number is contained within another. This method helps break down total sums into more digestible single-unit prices.

The division was carried out by inputting the total subscription cost and number of corresponding issues into a formula:
\[ \text{Cost per Issue} = \frac{\text{Total Subscription Cost}}{\text{Number of Issues}} \] By performing this operation for both subscription options, we could keenly compare prices on a per-issue basis. Simple mathematical operations like this make it easier to discern hidden savings or added costs of different monetary commitments. It's a vital tool for anyone who wants, not just to see numbers, but to understand them.