Problem 56 - Elementary Algebra

Question

Chicken-flavored rice contains 300 calories in each 2.5 -ounce serving. How many calories are in a 4-ounce scoop of chicken- flavored rice?

Step-by-Step Solution

Answer

A 4-ounce scoop contains 480 calories.

Step 1: Determine Calories Per Ounce

You are given that a 2.5-ounce serving of chicken-flavored rice contains 300 calories. To find out how many calories are in 1 ounce, divide the total calories by the number of ounces in the serving.\[ \text{Calories per ounce} = \frac{300 \text{ calories}}{2.5 \text{ ounces}} = 120 \text{ calories per ounce} \]

Step 2: Calculate Calories for 4 Ounces

Now that you know each ounce of chicken-flavored rice contains 120 calories, multiply this value by the number of ounces in the scoop you are considering, which is 4 ounces.\[ \text{Calories for 4 ounces} = 120 \text{ calories per ounce} \times 4 \text{ ounces} = 480 \text{ calories} \]

Key Concepts

Ratios

Ratios are an essential mathematical concept used to compare two quantities relative to each other. In the context of the exercise regarding calorie calculation for chicken-flavored rice, we start by looking at the ratio of calories to ounces.

• Example in the problem: 300 calories per 2.5 ounces

This ratio helps us understand how many calories are present in a specific portion of food. Understanding the initial ratio allows us to find the calories in different serving sizes by adjusting the quantities while maintaining the same ratio. This concept is fundamental not just in calorie calculations, but also in many daily activities such as cooking, where recipes treat ingredients in specific proportions.

Unit Conversion

Unit conversion involves changing one unit of measurement to another to make calculations easier or meet a specific requirement. In our exercise, we're converting the information from a 2.5-ounce serving to a 1-ounce serving, facilitating a direct calculation for any scoop size.

• Convert 300 calories/2.5 ounces to 120 calories/ounce

The conversion simplifies understanding and solving the problem, especially when different serving sizes are involved. Grasping the concept of unit conversion is crucial not only for math exercises but also in science and cooking, where measurements often need adjustments for correct application.

Multiplication

Multiplication is the mathematical operation used to scale numbers or amounts. Once we know the calories per ounce from the original ratio, we use multiplication to find out how many calories are in a 4-ounce scoop of rice.

• Calculate: 120 calories/ounce × 4 ounces

This calculation gives the total calorie intake for the larger portion. Multiplication is a straightforward process that enhances efficiency when scaling quantities. In calorie calculations, it allows for quick assessments of nutritional intake over varying serving sizes.

Division

Division is the process of distributing a single amount into multiple portions evenly. In the calorie calculation exercise, division is used to determine the calories per ounce from the total calories in a 2.5-ounce serving.

• Equation: 300 calories ÷ 2.5 ounces

This process breaks down the total calorie information into smaller, manageable parts, representing the caloric content of a single ounce. Division is pivotal for understanding proportional relationships and solving problems that require determining equal parts, especially in everyday scenarios like portion control in cooking and dividing resources evenly.