Problem 110 - Prealgebra

Question

The large health insurer Wellpoint, Inc., owner of Anthem Blue Cross, earned $536 million in the last three months of 2009. What was the average earnings per month for the insurer over that period? Round to the nearest million. Associated Press-Times-Standard 02/09/10 HHS secretary asks Anthem Blue Cross to justify rate hike.

Step-by-Step Solution

Answer

The average earnings per month is 179 million dollars.

Step 1: Identify total earnings and time period

The insurer, Wellpoint Inc., earned $536 million over the last three months of 2009. We are asked to find the average earnings per month during this period.

Step 2: Calculate the average earnings per month

To find the average earnings per month, divide the total earnings by the number of months: \[ \text{Average earnings per month} = \frac{536\text{ million}}{3 \text{ months}} \]

Step 3: Simplify the calculation

Perform the division: \[ \frac{536}{3} = 178.67 \] million. Since the problem asks for the result to be rounded to the nearest million, we round 178.67 to 179 million.

Step 4: Write the final result

The average earnings per month for Wellpoint Inc. over the last three months of 2009 is 179 million dollars, rounded to the nearest million.

Key Concepts

Rounding Numbers

Rounding numbers is an essential skill in everyday mathematics, especially when dealing with financial figures. When you round a number, you're adjusting it to a specified level of precision. For instance, if you have a number in the tenths column, you might want to round it to the nearest whole number. This is common when we want a less precise, but more manageable number.
When rounding to the nearest whole number:

• If the digit to the right of your rounding target is 5 or more, you round up.
• If it's less than 5, you round down.

In our example, we had 178.67. Looking at the tenths place, which is 6, we determine it is 5 or more, so we round up.
This gives us 179 million when rounded to the nearest million. Rounding makes it easier to communicate figures, especially in financial reports like those of Wellpoint, Inc.

Division in Arithmetic

Division is a fundamental operation in arithmetic. It helps break down a large quantity into smaller, equal parts. This is especially useful for calculating averages, which involve determining how much each share or unit gets in a total distribution.First, we identify the total amount and the number of parts, or units, to divide the total into.
For example, Wellpoint Inc.'s earnings were $536 million over three months. To find out the average, we divide the total earnings by 3 months:
\[ \text{Average earnings per month} = \frac{536 \text{ million}}{3 \text{ months}} \]
This results in an average of 178.67 million per month. Division tells us that if the total was evenly spread across the months, each would receive 178.67 million. This calculation is crucial for understanding averages in financial contexts.

Financial Mathematics

Financial mathematics involves using mathematical principles to solve problems related to finances such as managing budgets, forecasts, and profits. One common operation is calculating average earnings or revenue over a period, which is what we're exploring. Calculating an average helps us understand and communicate how a company's financial situation spreads evenly over time. In Wellpoint Inc.'s case, knowing the average earnings helps stakeholders assess monthly performance efficiently.
Here's a quick recap on calculating averages in finances:

• Identify the total sum of the financial figures in question (e.g., total earnings).
• Divide this total by the number of units involved (e.g., months).
• Round the result appropriately as needed by the context (e.g., to the nearest million).

These steps help ensure consistent and understandable financial reports, making decision-making more straightforward for investors, managers, and policy makers.