Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem18

Level 9&10 Video Solutions 2013 problem18

Video Transcription

Video Summary

Ivana wants to find five consecutive positive integers where the sum of three equals the sum of the other two. By defining the integers around a middle integer \(M\), the sums for both parts must be equal. The conditions reveal that \(M\) must be an even integer larger than 3, specifically \(M = 4\) or \(M = 6\). Thus, two sets of integers satisfy the conditions: starting sets {2, 3, 4, 5, 6} and {4, 5, 6, 7, 8}. Therefore, Ivana can write down 2 different sets of integers.

Keywords

consecutive integers

integer sum

middle integer

even integer

integer sets