Problem 98 - Elementary Algebra

Question

A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is \(27 \%\) of the \(\begin{array}{lll}\text { recommended } & \text { daily } & \text { amount. }\end{array}\) What is the total recommended daily amount of sodium?

Step-by-Step Solution

Answer

The total recommended daily amount of sodium is approximately 2407.41 mg.

Step 1: Identify Given Values

First, note that the grilled chicken salad contains 650 milligrams of sodium, which is 27% of the recommended daily amount.

Step 2: Set Up an Equation

Let the recommended daily amount of sodium be denoted as \( x \). The problem states that 650 mg is 27% of \( x \). This can be written as an equation: \[ 650 = 0.27x \]

Step 3: Solve for the Recommended Daily Amount

To find the total recommended daily amount of sodium, solve the equation \[ 650 = 0.27x \] by isolating \( x \). Divide both sides by 0.27: \[ x = \frac{650}{0.27} \]

Step 4: Calculate the Value of x

Perform the division to find \( x \): \[ x = \frac{650}{0.27} \approx 2407.41 \]

Step 5: Conclusion

The total recommended daily amount of sodium is approximately 2407.41 milligrams.

Key Concepts

Percentage Problems

Percentage problems are quite common in daily life and can be seen in various scenarios like discounts, interest rates, and even nutrition facts. When you deal with percentage problems, you often need to find a part, a whole, or a percentage rate itself.
For instance, if you know a part of something such as 650 mg of sodium, which is 27% of the recommended daily allowance, you can find the whole (the total recommended amount).
In general, when you're solving percentage problems, follow these steps:

• Identify the given values (part, whole, and percentage).
• Set up an equation that relates these values.
• Solve the equation for the unknown value.

In our problem, we knew the part (650 mg), and the percentage (27%), and were looking for the whole (recommended daily allowance of sodium).
This approach is very useful and can be applied to many real-world situations.

Algebraic Equations

Algebraic equations are mathematical statements that show the equality of two expressions. When solving algebraic equations, you're typically looking for the value of the unknown variable that makes the equation true.
To solve them, follow these basic steps:

• Identify the unknown variable (in our case, it's the recommended daily amount of sodium, let's call it x).
• Write an equation that represents the problem (we have: \[ 650 = 0.27x \]).
• Solve the equation by isolating the variable.

In our problem, we set up the equation \[ 650 = 0.27x \], and to solve it, we isolated x by dividing both sides by 0.27:
\[ x = \frac{650}{0.27} \]
Thus, this equation setup helps you find the value of x, which in this case is the total recommended daily allowance of sodium.

Recommended Daily Allowance

The recommended daily allowance (RDA) is a measure used in nutrition to recommend the amount of nutrients one should consume each day. It’s designed to meet the needs of nearly all healthy individuals in a particular age and gender group.
Understanding your RDA for nutrients like sodium can help maintain a healthy diet and prevent issues such as hypertension.
In our exercise, we used the concept of RDA to find the total recommended amount of sodium when given a portion (through the percentage provided).
If 650 mg is 27% of the recommended daily sodium intake, then you can use an algebraic equation to find the total amount:

• Set up the equation based on the percentage given: \[ 650 = 0.27x \]
• Solve for x to find the total RDA.

By solving the equation, we found that the recommended daily allowance of sodium is approximately 2407.41 mg.
This demonstrates how you can use percentages and algebra to determine nutritional guidelines that are essential for maintaining good health.