Problem 87 - Elementary Algebra

Question

Find the number of 1000 8-year-old children in the United States who have cerebral palsy. Round to the nearest tenth. Cerebral palsy is the most common motor disability in childhood, affecting approximately 1 in 303 8-year-old children in the U.S. (Source: www.cdc.gov, Aug. 29, 2011)

Step-by-Step Solution

Answer

3.3

Step 1: Understand the Given Information

The problem states that approximately 1 in 303 8-year-old children in the U.S. have cerebral palsy. This is the rate at which the condition occurs.

Step 2: Calculate the Rate

To find the number of children with cerebral palsy out of 1000, we need to set up a proportion based on the given rate. The rate is 1 in 303, which can be written as a fraction: \[ \frac{1}{303} \]

Step 3: Set Up the Proportion

Now, we set up a proportion where \[ \frac{1}{303} = \frac{x}{1000} \]. Here, x is the number of children with cerebral palsy among 1000 children.

Step 4: Solve the Proportion

To solve for x, cross-multiply and divide: \[ x = \frac{1}{303} \times 1000 \]. This simplifies to \[ x = \frac{1000}{303} \]

Step 5: Perform the Calculation

Divide 1000 by 303: \[ x = 3.3003 \].

Step 6: Round to the Nearest Tenth

Round 3.3003 to the nearest tenth. The rounded result is 3.3.

Key Concepts

Proportions

Proportions are equations that show two ratios are equal. They are a powerful tool for solving many types of problems, including those involving rates and percentages.

In this exercise, we use a proportion to find out how many 8-year-old children with cerebral palsy there are in a group of 1000 children. The problem states that the condition affects approximately 1 in 303 children. So, we set up a proportion: \[ \frac{1}{303} = \frac{x}{1000} \]

This proportion tells us that the ratio of affected children is the same, whether it is among 303 children or 1000 children. By solving this proportion, we can find the unknown value 'x', which represents the number of children with cerebral palsy out of the 1000 children considered.

Rounding Numbers

Rounding numbers is an important skill in everyday math. Rounding makes numbers easier to work with, especially when you don't need an exact answer. In our exercise, after we calculated the number of children with cerebral palsy, we obtained the value 3.3003.

To round this to the nearest tenth, we look at the digit in the hundredth place (which is the second digit to the right of the decimal point). In this case, it is a 0. Since 0 is less than 5, we do not round up the tenths place, and thus 3.3003 rounded to the nearest tenth is 3.3.

Remember:

• Round up if the digit is 5 or more
• Round down if the digit is less than 5

Basic Arithmetic

Basic arithmetic includes addition, subtraction, multiplication, and division. These are the building blocks for all other math topics. In this exercise, division plays a crucial role.

After setting up our proportion \[ \frac{1}{303} = \frac{x}{1000} \], we solve for 'x' by cross-multiplying and dividing: \[ x = \frac{1}{303} \times 1000 \]

This operation means that we multiply 1000 by the fraction \[ \frac{1}{303} \], which simplifies to \[ x = \frac{1000}{303} \]

Perform the division to find \[ x = 3.3003 \]

This calculation shows that we expect about 3.3 children with cerebral palsy out of every 1000 8-year-old children in the U.S. Being comfortable with basic arithmetic aids in more complex problem-solving scenarios.