Problem 73 - Elementary Algebra

Question

In a nutrition plan the ratio of calories to grams of carbohydrates is 16 to 1 . According to this ratio, how many grams of carbohydrates would be in a plan that has 2200 calories?

Step-by-Step Solution

Answer

137.5 grams of carbohydrates.

Step 1: Understanding the Ratio

The given problem states that the ratio of calories to grams of carbohydrates is 16 to 1. This means that for every 16 calories, there is 1 gram of carbohydrates.

Step 2: Setting Up the Equation

To find the grams of carbohydrates needed for 2200 calories, we set up an equation based on the ratio. Let the number of grams of carbohydrates be represented by \( x \). The equation based on the given ratio is \( \frac{2200}{x} = 16 \).

Step 3: Solving the Equation for Carbohydrates

Solve the equation \( \frac{2200}{x} = 16 \) to find \( x \). To do this, cross-multiply to get \( 2200 = 16x \).

Step 4: Isolating \( x \)

Divide both sides of the equation by 16 to solve for \( x \): \( x = \frac{2200}{16} \).

Step 5: Calculating the Result

Perform the division \( \frac{2200}{16} \) to find \( x = 137.5 \). Thus, 137.5 grams of carbohydrates are needed for 2200 calories.

Key Concepts

Understanding Calories

Calories are a measure of energy. In nutrition, they tell us how much energy our body might receive from consuming a particular food or meal.

Knowing the number of calories in your meals can help you maintain and regulate your energy balance. For instance, consuming more calories than your body needs could lead to weight gain, while consuming fewer could lead to weight loss.

• Calories are often used to understand and manage diet and nutritional needs.
• They are essential for performing daily activities and supporting metabolic processes.
• Different foods and nutrients contribute varying amounts of calories to your diet.

When planning meals or diets, it's crucial to consider both the quantity and quality of calories you're consuming. This helps ensure a balanced intake of nutrients for optimal health.

Carbohydrates in Nutrition

Carbohydrates are one of the primary nutrients found in our diet, often used by our bodies as a key source of energy. They are mostly found in foods like bread, pasta, fruits, and vegetables.

• Carbohydrates are converted into glucose, which our body uses as fuel for energy.
• They can be classified into simple and complex carbohydrates, affecting how quickly they release energy.
• Maintaining a balanced intake of carbohydrates is essential for sustained energy, especially important in sports and active lifestyles.

In a nutrition plan, the ratio of nutrients such as calories and carbohydrates plays a vital role. This ratio can help tailor diets to suit specific energy requirements and nutritional needs.

Solving Equations in Ratio Problems

Solving equations that involve ratios typically starts by understanding the relationship between different quantities. In nutrition, such equations often help balance diet components effectively.

• Start by identifying the ratio given, such as calories to carbohydrates.
• Set up an equation that models this relationship. In our exercise, the equation is \(\frac{2200}{x} = 16\).
• Use algebra to solve for the unknown variable. Here, it involves cross-multiplying to clear the fraction.
• Once simplified, isolate the variable by performing operations such as division, as shown with \(x = \frac{2200}{16}\).

This method provides a systematic approach to finding solutions involving proportional relationships, which is key in ensuring the effectiveness of nutritional plans.