Grades 7-8 Video Solutions 2026-2026_7-8

Video Transcription

Video Summary

Problem number 18. The units digit of a number is 1. Julia removes this digit by deleting it, forming a new number that is 2026 less than the original number. What is the sum of the digits of the original number? We know that this number is 4 digits, because deleting one digit made it a 4 digit number smaller. So let's write the original number as xyz1, and deleting the last digit gives xyz. This means that xyz1 minus xyz equals 2026. Let's look at the rightmost column. 1 minus z is 6. This is not usually possible, unless we borrow from the z in the first row. In that case, 11 minus z equals 6, so z equals 5. Now let's look at the second column from the right. It says 5 minus y equals 2. Remember though that we borrowed from this 5, so really it's a 4. 4 minus y equals 2, so y is equal to 2. Now let's look at this third column from the right. 2 minus x equals 0. We did not borrow from this 2, so this means x is just equal to 2. And this gives the full number. Originally it was 2251, and then we removed the last digit to get 225. The sum of the digits of the original number is 2 plus 5 plus 2 plus 1, or 10. So the answer is a, 10.

Keywords

number theory

digit deletion

place value

subtraction

sum of digits