Problem 37 - College Algebra and Calculus: An Applied Approach

Question

Comparing Calories A lunch consisting of a Big Mac, large fries, and large soft drink at McDonald's contains 1440 calories. A lunch consisting of a small hamburger, small fries, and a small soft drink at McDonald's contains 660 calories. Find the percent change in calories from the larger to the smaller lunch. (Source: McDonald's Corporation)

Step-by-Step Solution

Answer

The percent change in calories from the larger lunch to the smaller lunch is 54.16% decrease.

Step 1: Understand the problem

The problem involves finding the percent change in calories from a larger lunch to a smaller one. The total calories for the larger lunch is 1440 while for the smaller lunch is 660.

Step 2: Calculate the difference in calories

The difference in calories between the larger and smaller lunch is calculated by subtracting the calories of the smaller lunch from that of the larger lunch. Hence, Difference = Larger Lunch - Smaller Lunch calories = 1440 - 660 = 780 calories.

Step 3: Calculate the percentage change

The percentage change is calculated by dividing the change in calories by the original number of calories and then multiplying by 100. Hence, Percent Change = (Difference/Original)*100 = (780/1440)*100 = 54.16%. Therefore, there is a 54.16% decrease in calories when switching from larger lunch to the smaller lunch.

Key Concepts

Calorie Comparison

Understanding the nutritional content of meals, particularly in terms of calorie count, is a vital aspect of managing a healthy diet. When it comes to comparing the differences in calories between two food options, it's essential to look at the actual numbers and consider the impact on your dietary goals.

For example, if you were comparing a larger meal with a smaller meal at McDonald's, you'd discover that a Big Mac combo meal with large fries and a large soft drink contains 1440 calories, while the same meal in smaller portions only has 660 calories. This significant difference can affect your daily caloric intake, which is an important consideration for weight management and overall health. Through such a comparison, individuals can make more informed choices by opting for meals that suit their nutritional needs and caloric budgets.

Percentage Change Calculation

The calculation of percentage change is a mathematical operation that shows how much something has increased or decreased in comparison to its original value. It's expressed as a percentage and can be crucial in various fields, including finance, economics, and in this case, nutritional mathematics.

To calculate the percentage change when comparing two caloric values, such as in our McDonald's meal scenario, you subtract the smaller value from the larger to find the difference. Then, divide this difference by the original number (the larger meal's calories) and multiply the result by 100 to get the percentage decrease. This calculation is often used to determine the effect of different sizes or options on caloric intake and helps individuals understand the relative magnitude of changes in their diet choices.

Nutritional Mathematics

Nutritional mathematics is the application of mathematical principles to nutritional data, allowing individuals to track and manage their intake more effectively. This involves computations such as daily calorie needs, percentage of macronutrients, and as in our example, percentage change in calorie counts between different meal sizes.

For those watching their caloric intake, understanding how to apply these mathematical concepts can make it easier to navigate menu options and maintain a balanced diet. When one realizes that switching from a larger to a smaller meal at McDonald's results in a 54.16% decrease in calories consumed, this information can be incredibly valuable for dietary planning and informed decision-making in relation to personal health and nutrition goals.