THREE NUMBERS

Original Problem: Three numbers in a row have a sum of 9000. What are the numbers?


1. Problem Statement

This problem is called Three Numbers. The problem is to find three consecutive numbers with a sum of 9,000.

2. Process

I tried to solve the problem by working on simpler examples first. This is called the process of analogy. I also used estimation to get the final answer.

My First Idea

The first thing I tried was working out the problem for three numbers that add up to 9 instead of 9,000. That was easy 2 + 3 + 4 = 9. Then I thought I could just add three zeroes on the end of each number.

2,000 + 3,000 + 4,000 != 9,000

Oops! That didn't work because the three numbers were not consecutive.

A Better Idea

Then I tried something else. Consecutive numbers are almost the same size. If I estimated the sum of three consecutive numbers it would be about three times the middle one. Then I got it! 3,000 is one third of 9,000 so three numbers near 3,000 should add up to about 9,000.

I quickly wrote down 3,000 and 3,001 and 3,002 and thought I was done. Oops, again! They added up to 9,003. I had to make one of the numbers smaller but still keep them consecutive. So, I just moved each one down by 1.

My Answer

My three numbers were

2,999 + 3,000 + 3,001 = 9,000

3. Evaluation

I felt this problem was easy. I liked working on it because it was fun. The most difficult part was finding the lowest number. I learned that 2 consecutive numbers can only add up to an odd number. I'm proud that I finished the problem in one night.


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