Alice's Candy and Cookie Consumption: A Mathematical Puzzle

In this article, we explore a fun and engaging puzzle involving Alice's daily candy and cookie consumption. By solving algebraic equations and applying logical reasoning, we will determine how many cookies Alice ate today, providing readers with a practical example of mathematical problem-solving in everyday scenarios.

Introduction to the Problem

Alice consumed a specific number of candies and cookies each day. On one particular day, she ate 3 fewer candies than the previous day and twice as many cookies as the previous day. Interestingly, the total number of candies and cookies she ate on that day was the same as the total she consumed on the previous day. This article delves into the mathematical reasoning behind this intriguing situation and provides a step-by-step solution to finding out how many cookies Alice ate today.

Defining the Variables

We start by defining the variables to represent the quantities consumed:

Yesterday

x0 number of candies Alice ate yesterday y0 number of cookies Alice ate yesterday

Today

x1 number of candies Alice ate today y1 number of cookies Alice ate today

Formulating the Equations

Based on the problem statement, we can write down the following equations:

x1 x0 - 3 y1 2y0 x0 y0 x1 y1

Solving the Equations

Substituting the values of x1 and y1 into the third equation, we get:

x0 y0 (x0 - 3) 2y0

Simplifying the equation:

x0 y0 x0 - 3 2y0

Subtracting x0 from both sides:

y0 -3 2y0

Subtracting y0 from both sides:

-3 y0

Thus, y0 3.

Using y0 3, we substitute it back into the second equation to find:

y1 2 × 3 6.

Therefore, Alice ate 6 cookies today, and we can now verify our work:

Today: 6 cookies and 3 candies Yesterday: 3 cookies and 6 candies

a. Three fewer candies check: 6 3 3 - 3

b. Twice as many cookies check: 6 2 × 3

c. Same total each day check: 3 6 6 3

Conclusion

In this article, we have successfully solved the problem of Alice's candy and cookie consumption. By using algebraic equations and logical reasoning, we determined that Alice ate 6 cookies today, reinforcing our understanding of basic mathematical concepts and their real-world applications.