Problem 42 - Prealgebra

Question

Use the following information. (Lesson 1-3) Cornet Cable charges 32.50 dollars a month for basic cable television. Each premium channel selected costs an additional 4.95 dollars per month. How much does cable service cost per year if Abby subscribes to 3 premium channels?

Step-by-Step Solution

Answer

The cable service costs $568.20 per year if Abby subscribes to 3 premium channels.

Step 1: Identify Monthly Costs

First, determine the monthly cost of Abby's cable service. Cornet Cable charges $32.50 for the basic service. Abby has selected 3 premium channels, and each channel costs $4.95 per month. Multiply the number of channels, 3, by the cost of each channel, $4.95.

Step 2: Calculate Monthly Premium Cost

The monthly premium cost for 3 channels is calculated as follows:\[ 3 ext{ channels} \times 4.95 \,\text{dollars per channel} = 14.85 \,\text{dollars} \]

Step 3: Total Monthly Cost

Add the basic service charge to the total monthly cost of premium channels to find the total monthly cost:\[ 32.50 \,\text{dollars} + 14.85 \,\text{dollars} = 47.35 \,\text{dollars per month} \]

Step 4: Annual Cost Calculation

To find the yearly cost, multiply the total monthly cost by the number of months in a year:\[ 47.35 \,\text{dollars per month} \times 12 \,\text{months} = 568.20 \,\text{dollars per year} \]

Key Concepts

Monthly Costs Calculation

Calculating monthly expenses is an essential life skill. In the case of cable television, it's important to know both the base and additional costs.
For Abby, the basic cost is \(32.50 a month. But there's more than just the basic service.

• Abby adds on premium channels, each priced at \)4.95.
• If Abby chooses 3 premium channels, we multiply: \[3 \, \text{channels} \times 4.95 \, \text{dollars per channel} = 14.85 \, \text{dollars} \]

Now, add this premium cost to the basic cost to find the total monthly amount.
\[32.50 \, \text{dollars} + 14.85 \, \, \text{dollars} = 47.35 \, \text{dollars per month}\]
With this method, you can easily figure out what Abby will pay every month.

Annual Cost Calculation

Understanding annual costs helps with budget planning. Once you know a monthly cost, scaling it to a yearly figure is straightforward.

Simply multiply the monthly cost by 12, since there are 12 months in a year.
If Abby's monthly cost is \(47.35, compute the yearly cost like this:

• Multiply: \[47.35 \, \text{dollars per month} \times 12 \, \text{months} = 568.20 \, \text{dollars per year} \]

Now, Abby knows she needs to set aside \)568.20 every year for her cable service.
This clear method ensures that you always have a proper budget and don't get surprised by yearly expenses.

Mathematical Operations

Math shines when breaking down daily costs. It's about precision and understanding numbers.
Let's explore the mathematical operations used in these calculations.

• You start by multiplying. This finds the extra cost from premium channels. Multiply the number of channels by the cost per channel.
• Next, you add. This operation combines the base service cost with the calculated premium costs.
• Finally, multiply again. This time to scale the monthly sum to an annual figure.

These operations, when used correctly, help not only in solving textbook exercises but also in real-world financial planning.
Knowing when and how to use these operations allows you to gleefully tackle similar problems.