Problem 28 - Elementary Algebra

Question

In a sample of 920 children in Texas, ages \(24-35\) months, \(32.3 \%\) had received the hepatitis A vaccine. Find the number of children who received the vaccine. Round to the nearest whole number. (Source: www.cde.gov/nchs/ nis.htm, 2003)

Step-by-Step Solution

Answer

297 children received the vaccine.

Step 1 - Understand the problem

We need to find the number of children in a sample of 920 who received the hepatitis A vaccine, given that 32.3% of the children have been vaccinated.

Step 2 - Convert percentage to decimal

To perform calculations, convert the percentage to a decimal. Divide the percentage by 100: 32.3% = 0.323

Step 3 - Calculate the number of vaccinated children

Multiply the total number of children by the decimal form of the percentage to find the vaccinated children: Number of vaccinated children = 920 * 0.323

Step 4 - Perform the multiplication

Calculate the product: 920 * 0.323 = 297.16

Step 5 - Round to the nearest whole number

Since we need a whole number, round 297.16 to the nearest whole number: 297.16 rounds to 297

Key Concepts

percentage calculation

Percentage calculation is a very useful skill in many areas of math and everyday life. A percentage is a way of expressing a number as a fraction of 100. For example, 32.3% means 32.3 out of every 100. Percentages can be used to show how much of something exists compared to the whole.
In problems like this, always identify the percentage and the whole amount. Here, the problem gives us 32.3% of 920 children. This means we need to find out how many children this percentage represents.
Understanding this concept helps tackle various real-world problems, such as calculating discounts, interest rates, and statistics, just to name a few.

converting percentages to decimals

When working with percentages in calculations, it's important to convert them to decimal form. This makes the math easier. To convert a percentage to a decimal, divide the percentage by 100. Don't forget to adjust the decimal place accordingly. For example:
32.3% becomes 32.3 / 100 = 0.323.

When you do this, you transform the percentage value into something more usable for multiplication. Simply put, move the decimal point two places to the left.
This method applies universally, making it simple to switch between percentages and decimals, enhancing both your speed and accuracy in solving problems.

multiplication

Multiplication is one of the basic operations in mathematics. It involves finding the total of one number, referred to as the multiplicand, taken a specified number of times (multiplier). To find out how many children received the vaccine, multiply the total number of children (920) by the decimal form of the percentage (0.323).
Specifically, the calculation here is: 920 * 0.323.
Using multiplication in this way helps us determine quantities when given a part of a whole expressed as a percentage.
It's a common method in problems involving ratios, scaling, and more.

rounding numbers

Rounding numbers simplifies them while keeping their value close to what it was. It's often used to make lengthy decimals easier to work with. The rule of rounding is straightforward: if the digit following the place you're rounding to is 5 or higher, round up the last digit you're keeping by 1. If it's 4 or lower, keep the digit as is.
In our problem, after multiplying, we get 297.16. Here, we round to the nearest whole number, looking at 0.16:
- Since 6 (the digit after the decimal) is higher than 5, we round 297.16 up to 297.
Rounding is crucial for presenting answers in a more readable and practical form, especially when precision beyond a certain point isn't necessary.