Solving Math Puzzles with Logical Reasoning: A Bakery's Cupcake Sales

Math puzzles can be both challenging and rewarding. They offer a unique way to engage our minds, often requiring us to think logically and apply mathematical principles. In this article, we’ll dive into a typical math puzzle involving cupcakes sold by a bakery. By following a step-by-step approach, we will solve this puzzle and enhance our problem-solving skills. Let's break it down and find out how many cupcakes Mrs. C sold last week and this week.

Understanding the Problem

Let's begin with a clear understanding of the problem. Mrs. C is a baker who sells cupcakes. Last week, she sold 6 more than 3 times the number of cupcakes that she sold this week. Over the two weeks, she sold a total of 110 cupcakes. We need to determine how many cupcakes she sold last week and this week.

Setup the Equations

Let's use algebra to represent the problem. We will let x be the number of cupcakes sold this week. Therefore, last week she sold ( 3x 6 ) cupcakes. We know that the total sales over the two weeks amount to 110 cupcakes. We can set up the following equation to represent this:

[3x 6 x 110]

Simplify the equation by combining like terms:

[4x 6 110]

Subtract 6 from both sides to isolate the term involving x:

[4x 104]

Divide both sides by 4 to solve for x:

[x 26]

Hence, she sold 26 cupcakes this week. To find the number of cupcakes sold last week, we need to compute ( 3x 6 ):

[3 cdot 26 6 78 6 84]

So, Mrs. C sold 84 cupcakes last week and 26 cupcakes this week.

Logical Reasoning and Example Walkthrough

Let's revisit the problem step-by-step with a detailed walk-through:

Step 1: Let the number of cupcakes sold this week be ( x ). Step 2: According to the problem, the number of cupcakes sold last week is given by ( 3x 6 ). Step 3: The total number of cupcakes sold over the two weeks is 110. Therefore, we set up the equation: [x (3x 6) 110] Step 4: Combine like terms: [4x 6 110] Step 5: Subtract 6 from both sides: [4x 104] Step 6: Solve for ( x ) by dividing both sides by 4: [x 26]

Therefore, the number of cupcakes sold this week is 26. To find the number of cupcakes sold last week, we calculate:

[3 cdot 26 6 78 6 84]

So, the number of cupcakes sold last week is 84 and this week is 26.

Summary

Through logical reasoning and algebraic manipulation, we have been able to determine the number of cupcakes sold by Mrs. C over the two weeks. This problem not only involves basic algebra but also requires careful reading and comprehension of the given conditions. By breaking down the problem into simpler steps and using the power of equations, we can solve even the most complex math puzzles.

Conclusion

Math puzzles like the one involving the bakery's cupcake sales can enhance our problem-solving skills and logical reasoning. By following a methodical approach, we can efficiently solve these puzzles and gain confidence in our mathematical abilities. Give yourself a challenge and try solving other similar puzzles to further sharpen your skills!