Problem 95 - Elementary Algebra

Question

One serving of oatmeal has eight grams of fiber, which is \(33 \%\) of the recommended daily amount. What is the total recommended daily amount of fiber?

Step-by-Step Solution

Answer

The recommended daily amount of fiber is approximately 24.24 grams.

Step 1 - Understand the Given Information

One serving of oatmeal provides 8 grams of fiber, and this represents 33% of the recommended daily amount.

Step 2 - Formulate the Equation

Let the total recommended daily amount of fiber be represented by the variable \( x \). Since 8 grams is 33% of \( x \), we can write the equation as \[ 0.33x = 8 \].

Step 3 - Solve for x

To find \( x \), divide both sides of the equation by 0.33: \[ x = \frac{8}{0.33} \].

Step 4 - Calculate the Answer

Perform the division: \[ x = \frac{8}{0.33} \approx 24.24 \]. Thus, the total recommended daily amount of fiber is approximately 24.24 grams.

Key Concepts

Understanding Equations

Equations are mathematical statements that assert the equality of two expressions. In the problem, we used an equation to represent the relationship between the amount of fiber in one serving and the total recommended daily amount. Let's break it down further:

• We have 8 grams of fiber in one serving, which is 33% of the daily recommended amount.
• To translate this into an equation, we use the variable \( x \) to represent the total recommended daily amount of fiber.
• Since 8 grams is 33% of \( x \), we write: \( 0.33x = 8 \).

The next step is to solve for \( x \). We do this by isolating \( x \) on one side of the equation. This involves dividing both sides by 0.33, giving us \( x = \frac{8}{0.33} \), which simplifies to approximately 24.24 grams.

Mastering Percentage Calculations

Percentage calculations are vital in many fields, including nutrition, finance, and statistics. Here, we dealt with percentages to find out the total daily fiber recommendation. Here’s how it works:

• A percentage represents a fraction of 100. For example, 33% is 33 out of 100 or 0.33 when converted to a decimal.
• To find a percentage of a quantity, multiply the quantity by the decimal form of the percentage.
• In this problem, we knew that 8 grams is 33% of the recommended daily amount. This is why we wrote: \( 0.33x = 8 \). The 0.33 represents 33% and \( x \) is the total we are solving for.

By understanding how to manipulate percentages and convert them into equations, you can solve a wide range of real-world problems.

Applying Nutritional Mathematics

Nutritional mathematics plays a crucial role in determining dietary needs and ensuring balanced diets. Here’s how we applied it in this exercise:

• We were given a specific nutritional fact: one serving of oatmeal contains 8 grams of fiber, which is 33% of the daily recommended amount.
• Using this information, we set up an equation to find out the total recommended daily fiber intake.
• By solving the equation \( 0.33x = 8 \), we calculated the recommended daily amount to be approximately 24.24 grams.

This is a common method in nutritional science to ensure individuals get the right amount of nutrients. By understanding how to translate nutritional information into mathematical equations and solving them, you can make informed dietary choices and better understand food labels and nutritional guidelines.