Problem 96 - Elementary Algebra

Question

One serving of trail mix has 67 grams of carbohydrates, which is \(22 \%\) of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

Step-by-Step Solution

Answer

305 grams.

Step 1: Identify Given Information

One serving of trail mix contains 67 grams of carbohydrates. This quantity is given as 22% of the recommended daily amount.

Step 2: Set Up the Equation

To find the total recommended daily amount (let's call it X), knowing that 22% of X is equal to 67 grams, we set up the equation: \[ 0.22X = 67 \]

Step 3: Solve for X

To solve for X, isolate X by dividing both sides of the equation by 0.22: \[ X = \frac{67}{0.22} \]

Step 4: Calculate the Result

Solving the equation from the previous step, we get: \[ X = 304.545 \dots \approx 305 \] Therefore, the total recommended daily amount of carbohydrates is approximately 305 grams.

Key Concepts

Carbohydrate Calculation

Carbohydrates are a vital part of our diet, providing essential energy for our daily activities. In this problem, we are tasked with determining the total recommended daily amount of carbohydrates. We start by knowing that one serving of trail mix, which contains 67 grams of carbohydrates, accounts for 22% of the daily recommendation. By understanding percentages, we can set up an equation that allows us to calculate the total daily carbs. Here's how we approach it:

First, we recognize that the amount in one serving (67 grams) represents 22% of what we need daily. This can be expressed as an algebraic equation: 0.22 times the total daily amount equals 67 grams. Using basic algebra, we can solve this equation to find the total recommended intake.

Solving Linear Equations

Solving linear equations is a fundamental skill in algebra. In this scenario, solving for the total daily carbohydrate intake involves isolating the variable. We begin with the equation: \[ 0.22X = 67 \]

To isolate X, we divide both sides by 0.22: \[ X = \frac{67}{0.22} \]

This operation helps us find the value of X, which represents the total recommended daily carbohydrates. By performing the division, we calculate that X approximately equals 305 grams. Understanding steps like setting up equations from word problems and manipulating them to isolate variables is key to mastering linear equations.

Recommended Daily Values

Recommended daily values (RDVs) for nutrients like carbohydrates are guidelines provided to help us maintain a balanced diet. These values are often given as a percentage and represent the nutritional needs of the average person.

For carbohydrates, the recommended daily amount could vary slightly based on factors such as age, sex, and activity level. In this problem, the RDV is implied by the fact that 67 grams equals 22% of the total daily value.

By calculating the total recommended carbohydrate intake to be around 305 grams, we align with dietary norms which suggest that carbohydrates should constitute a significant portion of our caloric intake. Following RDVs helps ensure we're getting the proper nutrients to support our health and well-being.