Problem 23 - Basic College Mathematics

Question

Album Sales. There were 200.5 million music albums sold in \(2016 .\) Of these, 104.8 million were CDs. What percent of albums sold were CDs? Round to the nearest tenth of a percent. \([6.5 \mathrm{a}]\)

Step-by-Step Solution

Answer

52.3% of albums sold were CDs.

Step 1: Identify the Total Number of Albums Sold

The total number of music albums sold in 2016 is given as 200.5 million.

Step 2: Identify the Number of CDs Sold

The total number of CDs sold in 2016 is given as 104.8 million.

Step 3: Calculate the Percentage

To find the percentage of albums sold that were CDs, use the formula: \[ \text{Percentage of CDs} = \frac{\text{Number of CDs}}{\text{Total Number of Albums}} \times 100 \] Substitute the given values: \[ \text{Percentage of CDs} = \frac{104.8}{200.5} \times 100 \]

Step 4: Perform the Division

Calculate the division first: \[ \frac{104.8}{200.5} \ \text{This gives approximately } 0.5228 \]

Step 5: Multiply by 100

Next, multiply the result by 100 to convert it to a percentage: \[ 0.5228 \times 100 = 52.28 \]

Step 6: Round to the Nearest Tenth

Finally, round the result to the nearest tenth of a percent: \[ 52.28 \ \text{Rounding to the nearest tenth gives } 52.3 \]

Key Concepts

Album Sales

Music albums come in various formats, including CDs, vinyl, and digital downloads. In 2016, the total number of music albums sold was 200.5 million. Understanding how many of these albums were CDs is crucial for market analysis. It helps music producers and retailers strategize their production and sales approaches. In this problem, we focus on the CD format, which had a noticeable share of sales: 104.8 million out of the total albums sold.

Calculating Percentages

Percentages represent a part of a whole in a way that’s easy to understand. When you calculate a percentage, you’re finding out how much out of 100 something is. For example, to know the percentage of CDs sold out of total album sales, use this formula:

• Find the total: 200.5 million albums
• Find the portion: 104.8 million CDs
• Use the formula: \( \text{Percentage of CDs} = \frac{104.8}{200.5} \times 100 \)

This calculation shows what fraction of the overall sales were CDs.

Basic Mathematics

Doing these kinds of calculations involves basic mathematical skills.

• First, you need division. For example, \( \frac{104.8}{200.5} \) means dividing the number of CDs by the total number of albums. This results in approximately 0.5228.
• Second, multiply the result by 100 to convert it to a percentage: \( 0.5228 \times 100 = 52.28\text{ percent} \).

These elementary steps are key in calculating any percentage, not just album sales.

Rounding Numbers

Rounding numbers makes them simpler and easier to work with. In this problem, the percentage result 52.28 needs to be rounded to the nearest tenth. Here’s how rounding works:

• Look at the number in the hundredths place (second place after the decimal point)
• If it's 5 or higher, round the number in the tenths place (first number after the decimal) up by one
• If it's less than 5, leave the tenths place as it is

For our problem, 52.28 rounds to 52.3 percent because 8 (in the hundredths place) is more than 5. This simplifies the number while keeping it accurate.