Problem 57 - Elementary Algebra

Question

Find the number of 2350 individual policyholders who will have their premiums raised. Anthem Blue Cross, which plans to raise premiums for about four-fifths of the ... individual policyholders ... has outraged members, many of whom have ... price increases of more than 30 percent. (Source: www.sfgate.com, Feb. 11, 2009)

Step-by-Step Solution

Answer

1880 policyholders will have their premiums raised.

Step 1: Understand the Problem

Anthem Blue Cross plans to raise premiums for about four-fifths of its individual policyholders. There are 2350 individual policyholders in total.

Step 2: Identify the Fraction

The fraction of policyholders who will have their premiums raised is four-fifths, or \(\frac{4}{5}\).

Step 3: Calculate the Number of Affected Policyholders

Multiply the total number of policyholders (2350) by the fraction who will have their premiums raised: \(\frac{4}{5} \times 2350\).

Step 4: Perform the Multiplication

Calculate \(\frac{4}{5} \times 2350 = 1880\).

Key Concepts

Fractions in real life

Fractions are not just limited to math class. They appear in real life situations all the time! For example, when you have to split a pizza into equal parts or divide up chores among siblings, you are using fractions. In the context of the original exercise, fractions help quantify the portion of policyholders whose premiums will increase. Here’s another common scenario: If you spend two-thirds of your allowance on a toy, then you clearly understand how much of your allowance remains. Blocking out time in your day? That’s fractions, too. Understanding and using fractions can make your life a lot easier and organized.

Multiplication of fractions

Multiplying fractions may sound complicated, but it's quite simple! Let’s break it down. When you multiply a fraction by a whole number, you are finding that part of the whole number.
For example, multiplying \(\frac{4}{5} \) by 2350 means you want to find out how many policyholders are 4 out of every 5 from the total 2350.
To multiply \(\frac{4}{5} \) by 2350, you can either:

• Multiply 4 by 2350 and then divide by 5
• First divide 2350 by 5 and then multiply by 4

Both methods will give you the same result.
Let's see the math:
Using the first method: \[ \frac{4}{5} \times 2350 = \frac{4 \times 2350}{5} = \frac{9400}{5} = 1880 \]
Using the second method:\[ \frac{4}{5} \times 2350 = 4 \times \frac{2350}{5} = 4 \times 470 = 1880 \]
Therefore, 1880 policyholders will have their premiums raised.

Solving word problems

Word problems can use real-life situations to make math practice more engaging. Here’s a step-by-step way to solve them:

• Understand the Problem: First, read the entire problem carefully. Identify what is being asked.
• Identify Key Information: Extract important details, such as numbers and fractions, from the problem.
• Set Up the Equation: Translate the words into a math equation using the given information.
• Solve: Perform the math calculations step by step.
• Check Your Work: Make sure your answer makes sense in the context of the question.

Returning to the original exercise:

• We started by understanding that Anthem Blue Cross plans to raise premiums for four-fifths of the policyholders.
• Next, we identified the fraction as \(\frac{4}{5} \).
• We set up the multiplication equation: \(\frac{4}{5} \) of 2350.
• After performing the multiplication, we found that 1880 policyholders will have their premiums raised.

With practice, solving word problems becomes easier. Keep at it!