Problem 38 - College Algebra and Calculus: An Applied Approach

Question

Comparing Calories One slice (or one-tenth) of a 14-inch Little Caesars pizza with bacon, pepperoni, Italian sausage, and extra cheese has 315 calories. The same slice without the extra toppings has 200 calories. Find the percent change in calories from a slice with the extra toppings to a slice without them. (Source: Little Caesars)

Step-by-Step Solution

Answer

The percent change in calories from a slice of pizza with the extra toppings to a slice without them is approximately 36.51%.

Step 1: Determine Old and New Values

Identify the calories of a slice of pizza with extra toppings as the old value, 315 calories. The calories in a slice without the toppings are the new value, which is 200 calories.

Step 2: Calculate the Difference

Subtract the new value from the old value. The difference here would be \( 315 - 200 = 115 \) calories.

Step 3: Use Percent Change Formula

Next, divide the difference by the old value and multiply by 100% to get the percentage change. The formula would look like \( \frac{115}{315} * 100\% \)

Step 4: Do the Calculations

The result after doing the calculations is approximately 36.51%.

Key Concepts

Calorie Comparison

When we talk about calorie comparison, we are essentially looking at how the calorie content of two similar food items varies. This is very helpful, especially when trying to make healthier eating choices. In the problem at hand, we are comparing two types of pizza slices: one with extra toppings and another without.

The slice with the extra toppings contains 315 calories, that is our starting point for the comparison. The slice without extra toppings is lighter on the calories, containing only 200 calories. The difference between these calorie counts is key in figuring out how much impact the extra toppings have on the total calorie intake.

Mathematical Calculations

Mathematical calculations help us quantify and understand changes or differences in values numerically. In this problem, the process of finding how much the calorie count changes involves a simple subtraction.

We start by determining the difference in calories between the two pizza slices. This is done by subtracting the calories of the less calorie-rich slice (200 calories) from the one with more calories (315 calories). The calculation here is straightforward:

• 315 - 200 = 115 calories.

This means that the extra toppings contribute to an additional 115 calories to the pizza slice.

Percent Change Formula

The percent change formula is a common mathematical tool used to express the change between two values as a percentage. It's a helpful way to understand what portion of the original value has been added or reduced.

The formula is:

• \( \text{Percent Change} = \frac{\text{Difference}}{\text{Old Value}} \times 100\% \)

In this scenario, the old value is the calorie count with the extra toppings, and the difference is the 115 calories less when the toppings are removed. Plugging in the numbers, we get:

• \( \frac{115}{315} \times 100\% \)

This calculation provides us with the percentage change, which allows us to express the calorie reduction in terms of a percentage. It's a powerful tool for comparing the relative difference in calories.

Algebraic Problem Solving

Algebraic problem solving involves using mathematical operations to find unknown values or solve for specific variables. In the context of this exercise, we are solving for the percent change in calorie count using algebraic principles.

After identifying the old and new calorie values, and calculating their difference, it's all about applying the percent change formula correctly. We use basic algebra to rearrange numbers and perform the operations: subtracting, dividing, and multiplying to reach a solution. Following these steps accurately helps us arrive at approximately 36.51% decrease in calories when the extra toppings on the pizza slice are removed.

Algebra is essential for breaking down the problem into manageable parts, ensuring we execute each calculation correctly, and confirming our understanding of the concept of percent change.