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please answer this question.
( Enrichment question )
Q. A number is three times the sum of digits . Find the number .
Answers
U can understand by this.
Step-by-step explanation:
Very clearly note that for numbers (not so large) with more than 3 digits have their sum of digits as maximum 2 digit numbers.
For example 999" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">999999 is largest 3 digit number, sum of its digits is 27 , in fact the largest 12 digit number will have a 3 digit, digit sum the number999999999999" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">999999999999999999999999 has digit sum equal to 108 so it will be sufficient to look for two digit and three digit numbers with given property.
Let two digit number be xy" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">xyxy written in decimal notation then we want 10x+y=3(x+y)" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">10x+y=3(x+y)10x+y=3(x+y)where x and y are whole numbers less than 10 which is equivalent to 7x=2y" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">7x=2y7x=2y under the constraints this means y=7,x=2" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">y=7,x=2y=7,x=2 remember we want whole number solutions less than 10 (single digit)(The general solution in integers is x=2kandy=7kkisanintegr" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">x=2kandy=7kkisanintegrx=2kandy=7kkisanintegr .So among two digit numbers 27 satisfies , one could guess this too. I was also thinking about negative numbers that could satisfy but we don't take digits negative by definition hence a positive (sum of digits ) can not be equal to a negative ( the number).further note that 0 is also a solution.
For three digit numbers we know the maximum value of sum of digits is 27 it's thrice will be 81 which is not a 3 digit numbe hence no 3 digits number satisfies ,so only 27 and 0 are solutions