Problem 14 - Prealgebra

Question

Tyler purchased 3 CDs for \(\$ 13\) each and 2 digital songs for \(\$ 0.99\) each. Write and then evaluate an expression for the total cost.

Step-by-Step Solution

Answer

The total cost is 40.98 dollars.

Step 1: Determine the Cost of the CDs

Find the total cost for the CDs by multiplying the price of one CD, which is 13 dollars, by the number of CDs, which is 3. This calculation is: \[3 imes 13 = 39\]So, the cost of the CDs is 39 dollars.

Step 2: Determine the Cost of the Digital Songs

Find the total cost for the songs by multiplying the price of one song, which is 0.99 dollars, by the number of songs, which is 2. This calculation is: \[2 imes 0.99 = 1.98\]So, the cost of the songs is 1.98 dollars.

Step 3: Add the Costs Together

Add the costs of the CDs and the digital songs together to find the total cost. The total cost is given by: \[39 + 1.98 = 40.98\]Thus, the total cost of the CDs and songs is 40.98 dollars.

Key Concepts

Understanding Multiplication in Cost Calculation

Multiplication is an essential arithmetic operation that helps us determine the total cost of multiple items. Whenever you need to find the total cost for several identical items, you use multiplication.
For instance, in our exercise, Tyler bought 3 CDs. Each CD costs \( \\(13 \). To find out how much he spent altogether on the CDs, you multiply the number of CDs by the price of one CD:

• 3 CDs at \( \\)13 \) each
• \[ 3 \times 13 = 39 \] dollars

This result tells us that Tyler spent a total of \( \\(39 \) on the CDs.
Similarly, Tyler purchased 2 digital songs. Each digital song is priced at \( \\)0.99 \). Again, you multiply:

• 2 digital songs at \( \\(0.99 \) each
• \[ 2 \times 0.99 = 1.98 \] dollars

Tyler's expense on digital songs totals \( \\)1.98 \).
By understanding multiplication, you can quickly calculate the cost of purchasing multiple items without having to add the same number repeatedly.

How Addition Helps Sum Up Costs

Addition is another core arithmetic operation that allows us to find the total by combining different amounts. Once you have calculated separate costs using multiplication, addition helps you sum them up.
In our scenario, Tyler's purchases include both CDs and digital songs. Calculating each separately gives:

• CDs cost \( \\(39 \)
• Digital songs cost \( \\)1.98 \)

To find out the total expenditure, add these amounts together:

• \[ 39 + 1.98 = 40.98 \] dollars

This sum represents the total cost Tyler needs to pay for all the items he purchased, which is \( \$40.98 \). Addition combines the results from our multiplication steps to give a complete picture of the total cost.

Applying Cost Calculation in Real Life

Cost calculation is a practical skill used often in everyday life, from shopping trips to budgeting expenses. It involves both multiplication and addition to find the total costs of multiple items or services.
Here’s how it works:

• First, decide the number of each item you are purchasing.
• Use multiplication to find the cost for each type of item. Multiply the quantity by the unit price.
• Then, use addition to combine the total costs of all different types of items.

In the exercise, we calculated costs for CDs and digital songs separately using multiplication, then combined them with addition. This approach can be applied to various purchasing decisions, ensuring you stay aware of your spending.
This method not only helps in individual purchase calculations but is an integral part of managing budgets and understanding financial responsibilities. Practicing these skills can lead to better financial planning and informed spending decisions.