Problem 69 - Fundamentals of Mathematics

Question

The number of nursing and related care facilities in the United States in 1971 was \(22,004 .\) In 1978 , the number was 18,722 . What was the total number of facilities for both 1971 and \(1978 ?\)

Step-by-Step Solution

Answer

The total number of facilities in 1971 and 1978 was 40,726.

Step 1: Understanding the Problem

The problem provides the number of nursing and related care facilities in two different years, 1971 and 1978. We are asked to find the total number of facilities for both these years combined.

Step 2: Identify Known Values

Identify and write down the values provided in the problem: the number of facilities in 1971 is 22,004 and in 1978 is 18,722.

Step 3: Set Up the Addition

To find the total number of facilities for 1971 and 1978, we need to sum the two numbers: 22,004 and 18,722.

Step 4: Perform the Addition

Add the two numbers together: \[ 22,004 + 18,722 = 40,726 \]

Step 5: Verify the Result

Double-check the addition to ensure there are no errors. The total of 40,726 represents the combined number of facilities in 1971 and 1978.

Key Concepts

Nursing Facilities

Nursing facilities play an essential role in providing care for individuals who require assistance with daily activities due to age, illness, or disabilities. These facilities offer a range of services such as:

• Long-term care for chronic illnesses
• Rehabilitation services for recovery after surgery
• Specialized care for conditions like Alzheimer's disease

Understanding the number of nursing facilities available is crucial for healthcare planning and resource allocation.
Supplying accurate data about these facilities helps to assess whether they meet community needs effectively and efficiently. The given exercise illustrates how changes in the number of facilities over time can be measured and tracked.

Problem Solving

Problem-solving is a critical skill that involves identifying, analyzing, and solving problems effectively. In the given exercise, problem-solving skills are applied to find the total number of nursing facilities across two different years.
Here’s a simplified problem-solving process:

• Identify the problem: Determine what you need to find — in this instance, the total number of facilities.
• Determine the known values: Recognize and gather all the data given, such as the facility numbers for the years 1971 and 1978.
• Choose the solution method: Decide on the method to solve the problem — addition is needed here.
• Execute the method: Carry out the addition process.
• Verify your result: Ensure the solution is correct by reviewing the steps.

Developing problem-solving skills enhances one's ability to approach a diverse range of challenges effectively.

Arithmetic Operations

Arithmetic operations form the basis of mathematics and include addition, subtraction, multiplication, and division. In this exercise, we focus on addition to combine two values representing nursing facilities. Addition is the process of calculating the total by combining numbers. Here’s how it works:

• Set up: Align the numbers vertically, ensuring the digits are in the correct columns (units, tens, hundreds, etc.). For 22,004 and 18,722, ensure each digit from both numbers is lined up appropriately.
• Start adding from the right: Begin with the rightmost column and proceed to the left, carrying over any value if the sum of digits in a column exceeds 9.
• Result: Finish with the total amount, 40,726, in this case.

Understanding and practicing arithmetic operations like addition enables students to solve a variety of everyday mathematical problems confidently.