Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

Video Summary

There are 20 three-digit positive integers \( x \) that satisfy the given conditions. Integers \( x \) are represented as 340 to 349 and 680 to 689. The process involves subtracting the sum of the digits of \( x \) from \( x \) to yield another three-digit number whose digits are all the same. The possible results of this subtraction are 333 or 666. By systematically choosing feasible \( a \) and \( b \) values (where \( a = 3, b = 4 \) and \( a = 6, b = 8 \)), each scenario provides 10 possible \( x \) values, resulting in 20 solutions overall.

Keywords

three-digit integers

digit subtraction

333

666

solutions