Problem 36 - Elementary Algebra

Question

The cost to buy a phone with a 2 -year service contract is \(\$ 199\). A single- line voice plan costs \(\$ 69.99\) per month. A 2 GB data plan is an additional \(\$ 30\) per month. An unlimited messaging plan is an additional \(20 per month. A case is \)35. Find the total cost to buy this phone and a case and to use the given plans for 2 years.

Step-by-Step Solution

Answer

To buy the phone, a case, and use the plans for 2 years, the total cost is \(\$3113.76\).

Step 1: Identify One-time Costs

First, list the one-time costs. The phone costs \(\$199\) and the case costs \(\$35\). Add these together: \(199 + 35 = 234\). Thus, the total one-time cost is \(\$234\).

Step 2: Identify Monthly Costs

Next, list the monthly costs for the services. The voice plan costs \(\$69.99\) per month, the data plan costs \(\$30\) per month, and the messaging plan costs \(\$20\) per month. Add these together: \(69.99 + 30 + 20 = 119.99\). Thus, the total monthly cost is \(\$119.99\).

Step 3: Calculate Total Monthly Cost for 2 Years

Multiply the total monthly cost by the number of months in 2 years (24 months). Therefore, \(119.99 \times 24 = 2879.76\). Thus, the total cost for 2 years of service is \(\$2879.76\).

Step 4: Calculate Total Cost

Finally, add the one-time costs (Step 1) and the total 2-year service cost (Step 3): \(234 + 2879.76 = 3113.76\). Thus, the total cost to buy the phone, a case, and use the given plans for 2 years is \(\$3113.76\).

Key Concepts

one-time costs

In this exercise, one-time costs are those that you only pay once and not every month. For a phone service, these costs include the price of the phone and any accessories, like a case. In our example, the phone costs \$199\ and the case costs \$35\. To find the total one-time cost, we need to add these two amounts together: \[199 + 35 = 234\]. So, the total one-time cost is \$234\.

monthly costs

Monthly costs are those you pay every month for the duration of the contract. For a phone service, these might include the costs for voice plans, data plans, and messaging plans. In our example, the costs are:

• Voice plan: \$69.99\ per month
• Data plan: \$30\ per month
• Messaging plan: \$20\ per month

To find the total monthly cost, we add these amounts together: \[69.99 + 30 + 20 = 119.99\]. Thus, the total monthly cost for our service plan is \$119.99\.

multiplication

Multiplication is a mathematical operation used to calculate total costs over multiple periods, like months or years. In our example, we need to find the total cost for 2 years of service at a monthly cost of \$119.99\. There are 24 months in 2 years, so we multiply the monthly cost by 24: \[119.99 \times 24 = 2879.76\]. This calculation gives us the total cost for 2 years of service, which is \$2879.76\.

addition

Addition is a basic mathematical operation used to combine different costs. To find the overall total cost, we need to add the one-time costs and the total monthly costs for 2 years. We already calculated the one-time costs as \$234\ and the total monthly cost for 2 years as \$2879.76\. Adding these together: \[234 + 2879.76 = 3113.76\]. Therefore, the total cost to buy the phone, a case, and use the given plans for 2 years is \$3113.76\.