Grades 7-8 Video Solutions 2021-video 2021 7-8/23

Video Transcription

Question 23. The six digit number 2 a b c d e is multiplied by 3 and the result is the six digit number a b c d e 2. What is the sum of the digits of this  number? So we can write down our number 2 a b c d e and multiply it by 3. Now we can begin with multiplying e times 3 and we know that this will give us  something ending with a 2. The only one digit answer for e is 4. 4 times 3 is equal to 12 which fits since we know that 2 has to be on the bottom. So we can  substitute out e for 4 and do the same on the bottom and then we carry over the 1. Now we have to do 3 times d and then plus 1 is equal to a number ending with  4. Subtract over the 1 and we get d times 3 is equal to a number ending with 3. The only way to do this with d being a one digit number is making it 1. So we  can replace our d's with 1's. Next we will do c times 3 will equal something ending with 1. The only way we can do this while making c a one digit number  is by making it 7. 7 times 3 is equal to 21. So we can replace the c's with 7's and we have to carry over the 2. We will repeat this process and do 3 times b  is equal to a number ending with 7 after we add 2. We subtract the 2 and we have b times 3 equals something ending with 5. The only number that b can be  while being a one digit number will be 5. 5 times 3 is equal to 15. So we can replace our b's with 5's. Our final step is a times 3 plus 1 will equal a  number ending with 5. We subtract the 1 and we have a times 3 equals a number ending with 4. The only solution for this is to make a equal 8 and then we get the  result of 24. We can replace our a's with 8's and then carry over the 2. So we get a total of 857,142. Now the question wanted us to find the sum of the digits  of this number. When we do 8 plus 5 plus 7 plus 1 plus 4 plus 2 we get our answer which is b, 27.

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