Problem 94 - Algebra for College Students

Question

After dieting for 30 days, Ignacio has lost 18 pounds. What number describes his average weight change per day?

Step-by-Step Solution

Answer

Ignacio's average weight loss per day is 0.6 pounds.

Step 1: Identify the Total Weight Change

Ignacio lost a total of 18 pounds after dieting for 30 days.

Step 2: Determine the Duration

The duration of the dieting period is 30 days.

Step 3: Calculate the Average Daily Weight Change

Use the formula for average change: \( \text{Average change per day} = \frac{\text{Total weight change}}{\text{Number of days}} \). Substitute the known values: \( \frac{18}{30} = 0.6 \).

Step 4: Interpret the Result

Since Ignacio lost weight, the average weight change per day is a decrease of 0.6 pounds per day.

Key Concepts

Understanding Weight Loss

Weight loss is a common health goal for many individuals and involves reducing body mass over a period of time. It usually results from reducing calorie intake and increasing physical activity. In the context of our exercise, Ignacio's 18-pound weight loss over 30 days reflects his efforts and changes in lifestyle. To effectively track such progress, it's useful to determine the average rate of change, which in this case is represented by his average weight loss per day.

• Weight loss is measured in pounds or kilograms.
• It's the result of consuming fewer calories than your body burns.
• The process involves monitoring food intake and activity levels.

Understanding these basics helps in setting realistic weight loss goals and assessing whether one's efforts are yielding the desired outcomes. Calculating the daily average loss can offer insight into the consistency and sustainability of a weight loss plan.

Exploring Mathematical Reasoning

Mathematical reasoning is fundamental in solving problems like determining the average weight change. It involves logical thinking and the application of mathematical concepts to arrive at a solution. For Ignacio's weight loss exercise, mathematical reasoning helps in using data correctly to calculate an average change.

• Start by identifying the total change, which in this case is 18 pounds.
• Next, determine the time period over which this change occurred - 30 days.
• Apply logical steps to calculate averages, illustrating clear and purposeful reasoning.

By logically determining each component of the problem and how they relate, mathematical reasoning ensures accuracy and clarity in calculations. It's a skill that hones critical thinking, helping students not only in academic tasks but also in making informed decisions in everyday life.

Applying Ratios and Proportions

Ratios and proportions are potent mathematical tools used to compare quantities. In Ignacio's weight loss case, we treat his total weight loss over 30 days as a ratio, helping us understand his progress better. The ratio expresses how much weight is lost in a single day out of the total number of days.

• A ratio is expressed as two numbers separated by a colon or as a fraction.
• The ratio in Ignacio's exercise is 18:30 or \(\frac{18}{30}\).
• This simplifies to 0.6, meaning he lost an average of 0.6 pounds each day.

By simplifying the ratio to its lowest terms, proportions help to articulate the relationship between two quantities clearly and concisely, allowing better insight into trends and metrics within the context provided.