Problem 43 - Algebra 2

Question

Megan exercises every morning for 40 minutes. She does a combination of step aerobics, which burns about 11 Calories per minute, and stretching, which burns about 4 Calories per minute. Her goal is to burn 335 Calories during her routine. Write a system of equations that represents Megan’s morning workout.

Step-by-Step Solution

Answer

The system of equations is \( x + y = 40 \) and \( 11x + 4y = 335 \).

Step 1: Define the variables

Call the number of minutes Megan spends on step aerobics as \( x \) and the number of minutes she spends on stretching as \( y \).

Step 2: Set up the time equation

Megan exercises every morning for a total of 40 minutes. This can be expressed as the equation: \( x + y = 40 \).

Step 3: Set up the calorie equation

Megan burns 11 Calories per minute during step aerobics and 4 Calories per minute during stretching. She wants to burn 335 Calories total, which gives the equation: \( 11x + 4y = 335 \).

Step 4: Write the system of equations

The two equations formed in Steps 2 and 3 are the system of equations representing Megan's workout: 1. \( x + y = 40 \)2. \( 11x + 4y = 335 \)

Key Concepts

Calories Burned

When you exercise, your body uses energy, which we often measure in calories. Calories are units of energy that help fuel all the activities your body performs. During physical activity, the rate at which you burn calories depends on the intensity and type of exercise involved. In our original exercise, Megan burns different amounts of calories per minute depending on the activity she's doing:

• Step Aerobics: Burns about 11 calories per minute. This is a more intense workout, so it expends more energy.
• Stretching: Burns about 4 calories per minute. Stretching is less intense and so uses less energy compared to aerobics.

By understanding these rates, you can determine how many total calories you burn based on the duration of each activity. This is crucial for creating a balanced exercise regimen that helps achieve specific fitness goals, like Megan's goal to burn 335 calories in her workout filled with a mix of aerobics and stretching.

Exercise Routine

An exercise routine is a planned schedule of physical activities designed to achieve specific fitness goals. By following a routine, like Megan does, you can ensure consistency and progress in your fitness journey. Let's understand her routine more clearly.
Megan's workout consists of two main activities: step aerobics and stretching. This combination provides both intense cardiovascular workout and the benefits of flexibility exercises.

• Consistency: Megan does her exercises every morning for 40 minutes. Consistency in exercise is key to achieving fitness goals.
• Variety: Combining different exercises, like aerobics and stretching, can help improve different aspects of fitness, balance and prevent boredom.

Overall, a well-thought-out routine can help you efficiently burn the calories you aim for, improve fitness, and maintain motivation to exercise regularly.

Variables in Equations

Variables are symbols used to represent quantities that can change or vary. In the context of the exercise, variables help us formulate and solve an exercise problem mathematically.
In Megan's case, we use the variables to represent the time she spends on each exercise:

• \( x \): Represents the number of minutes spent on step aerobics.
• \( y \): Represents the number of minutes spent on stretching.

To set up a system of equations, each aspect of the problem is expressed in a mathematical form. For Megan:

• The total exercise time is fixed at 40 minutes, leading to the equation: \( x + y = 40 \).
• The calorie goal is 335 calories, forming the equation: \( 11x + 4y = 335 \).

These equations can be solved simultaneously to find specific values of \( x \) and \( y \), helping Megan meet her exercise and calorie goals efficiently. Understanding how variables work in equations allows you to apply mathematical reasoning to a wide range of real-life situations.