Problem 106 - Elementary Algebra

Question

The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?

Step-by-Step Solution

Answer

60% of the total calories are from fat.

Step 1: Identify the Given Information

Identify the total calories and the calories from fat. From the problem, the total calories are 190 and the calories from fat are 114.

Step 2: Write the Formula for Percent Calculation

The formula to calculate the percentage of calories from fat is: \ \[ \text{Percentage} = \frac{\text{Calories from Fat}}{\text{Total Calories}} \times 100 \ \]

Step 3: Substitute the Values

Plug the given values into the formula: \ \[ \text{Percentage} = \frac{114}{190} \times 100 \ \]

Step 4: Perform the Calculation

Calculate the fraction first: \ \ \[ \frac{114}{190} \ \approx 0.6 \ \] Then multiply by 100 to convert to a percentage: \ \[ 0.6 \times 100 = 60 \ \]

Step 5: State the Final Answer

The final percentage of the total calories that is from fat is 60%.

Key Concepts

Nutrition Facts

Nutrition facts are a summary of information about the nutritional content of food. They help you understand the health implications of what you eat.
Key elements often include:

• Calories: The total energy content.
• Macronutrients: Amounts of fats, proteins, and carbohydrates.
• Micronutrients: Details of vitamins and minerals.

When you read a nutrition facts label, you can make better choices about what to eat by comparing the listed content.

Calories

Calories are units of energy. They measure how much energy you get from food. When you eat food, your body breaks it down to release energy. Here are some quick facts about calories:

• 1 gram of fat = 9 calories.
• 1 gram of protein = 4 calories.
• 1 gram of carbohydrate = 4 calories.

Knowing how many calories are in your food can help you maintain or achieve a healthy weight.

Fat Percentage

Fat percentage tells you how much of the total calories comes from fat. This is important for managing dietary fat intake, which affects heart health and weight. In our example, we calculate the percentage as follows:
Step-by-step:

• Find out how many calories are from fat: 114 calories
• Find the total number of calories: 190 calories
• Use the formula: \[ \text{Percentage} = \frac{\text{Calories from Fat}}{\text{Total Calories}} \times 100 \]
• Plug in the numbers: \[ \text{Percentage} = \frac{114}{190} \times 100 \]
• Simplify the fraction: \[ \frac{114}{190} \approx 0.6 \]
• Convert to a percentage: 0.6 \times 100 = 60%

Therefore, 60% of the calories in the chicken nuggets come from fat.

Basic Algebra

Basic algebra involves solving equations and working with variables. It helps us solve for unknowns.
In our problem: We used the formula for percentage calculation, which is: \[ \text{Percentage} = \frac{\text{Calories from Fat}}{\text{Total Calories}} \times 100 \] This is an example of an algebraic equation. Here’s how we solved it:

• Placed the given values into the equation.
• Simplified the fraction.
• Multiplied by 100 to convert the decimal to a percentage.

By understanding basic algebra, you can easily manipulate these equations to find what you need.