Solving a School Bazaar Cookie Selling Dilemma: Unravel the Math with Ease
Welcome to a practical exploration of solving an intriguing math problem related to a school bazaar. This problem focuses on the sales figures of two participants, Donny and Enda, who sold cookies. Understanding the relationship between their sales and applying basic mathematical principles can help us find the answer to the question at hand.
The Cognitive Challenge
Let's dive into the problem statement: Donny sold three times as many cookies as Enda during a school bazaar. Together, they sold an average of 140 cookies. The goal is to determine how many more cookies Donny sold compared to Enda.
Breaking Down the Problem: A Step-by-Step Analysis
Step 1: Calculate the Total Number of Cookies Sold
The first step involves understanding that the average of two persons is 140 cookies. Since both Donny and Enda are the only participants in this problem, the total cookies sold by both of them can be calculated as follows:
Total cookies sold Average cookies sold times; Number of participants
Total cookies sold 140 times; 2 280 cookies
Step 2: Establish the Relationship Between Donny's and Enda's Sales
The problem states that Donny sold three times as many cookies as Enda. Let's denote the number of cookies Enda sold as x. Consequently, the number of cookies Donny sold would be 3x.
Total cookies sold Number of cookies Enda sold Number of cookies Donny sold
280 x 3x
4x 280
Step 3: Solve for the Value of x
To find x, we perform the following division:
x 280 / 4 70
This tells us that Enda sold 70 cookies. Therefore, Donny, who sold three times as many cookies as Enda, can be calculated as:
Donny's sales 3x 3 times; 70 210 cookies
Step 4: Determine the Difference in Sales
The final step is to find out how many more cookies Donny sold than Enda:
Donny sold 210 cookies, and Enda sold 70 cookies.
The difference is: 210 - 70 140 cookies
Summary and Recap
To summarize, we calculated the total sales from the average and used the relationship between Donny's and Enda's sales to determine the exact numbers. Donny sold 210 cookies, while Enda sold 70 cookies. The difference in sales was 140 cookies, thus providing a clear and concise solution to this math problem.
Additional Insights
This problem-solving approach can be extended to other real-world scenarios involving ratios and averages. By understanding the principles involved, you can apply similar logic to solve various similar problems or real-life situations where such relationships need to be quantified.