Pizza Puzzle: Who Ate the Most?

The scenario presents a common problem encountered in household settings - sharing a pizza among siblings. Let's dive into the details and determine how much each sibling ate and the sequence in terms of the amount consumed.

Understanding the Problem

Four siblings, Alex, Beth, Cyril, and Dan, ordered a large pizza. Each sibling ate a portion of the pizza based on a fraction of the total. The fractions are as follows:

Alex ate 1/5 of the pizza. Beth ate 1/3 of the pizza. Cyril ate 1/4 of the pizza. Dan got the leftovers.

Calculation of Each Sibling's Share

To solve the puzzle, we need to calculate the exact amount each sibling ate in terms of a fraction of the whole pizza. Let's start by adding the fractions:

$$1 - left(frac{1}{5} frac{1}{3} frac{1}{4}right)$$

First, find a common denominator for the fractions:

$$1 - left(frac{12}{60} frac{20}{60} frac{15}{60}right)$$

Adding the fractions:

$$1 - left(frac{12 20 15}{60}right)$$

Which simplifies to:

$$1 - frac{47}{60} frac{13}{60}$$

This means Dan got 13/60 of the pizza.

Decomposing the Puzzle

Let's break it down further:

Alex ate 12/60 (1/5) of the pizza. Beth ate 20/60 (1/3) of the pizza. Cyril ate 15/60 (1/4) of the pizza. Dan ate 13/60 of the pizza.

Given these fractions, we can now rank the siblings based on the portion of pizza they consumed.

Ranking the Siblings

The sequence of the siblings in decreasing order of the part of the pizza they consumed is as follows:

Beth (20/60 or 1/3 of the pizza) Cyril (15/60 or 1/4 of the pizza) Dan (13/60 of the pizza) Alex (12/60 or 1/5 of the pizza)

This ranking shows that Beth consumed the most pizza, followed by Cyril, Dan, and Alex.

Closer Examination with Pizza Slices

For a more visual and practical approach, let's assume the pizza is cut into 60 slices. The distribution of slices among the siblings would be:

Alex ate 12 slices. Beth ate 20 slices. Cyril ate 15 slices. Dan ate 13 slices.

And hence, the final list of who ate most to least is:

Beth Cyril Dan Alex

Conclusion

The problem of determining the sequence based on the fractions consumed by each sibling is solved through accurate calculation and logical reasoning. Understanding the distribution of fractions is key to resolving such puzzles. Whether via abstract fractions or visual representations, the result remains consistent.