SOLUTION: The sum of the digits of a two-digit number equals 1/7 of the number. If the digits are reversed, the new number is 27 less than the original number. Find the original number.

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 Click here to see ALL problems on Miscellaneous Word Problems Question 77841: The sum of the digits of a two-digit number equals 1/7 of the number. If the digits are reversed, the new number is 27 less than the original number. Find the original number.Answer by ptaylor(2048)   (Show Source): You can put this solution on YOUR website!Let 10x+y=the number We are told that x+y=(1/7)(10x+y)----------------eq 1 We are also told that: 10y+x=(10x+y)-27----------------------------------eq 2 Simplifying eq 1: x+y=(10/7)x+(1/7)y multiply each term by 7 7x+7y=10x+y subtract 10x and also y from both sides 7x-10x+7y-y=10x-10x+y-y collect like terms -3x+6y=0 subtract 6y from both sides and divide both sides by -3 x=2y---------------------------eq 1 simplified Simplifying eq 2: 10y+x=10x+y-27 subtract 10x and also y from both sides 10y-y+x-10x=10x-10x+y-y-27 collect like terms 9y-9x=-27 multiply each term by -1 and divide each term by 9 x-y=3--------------------------------eq 2 simplified Substitute x=2y from eq 1 into eq 2 2y-y=3 or y=3--------------substitute into eq 1 x=2y=2*3=6 10x+y=60+3=63---------------------------the number CK sum of the digits of the number (6+3) = 1/7 of the number 9=1/7(63)--------------ok If the digits are reversed, the new number is 27 less than the original number: 36=63-27 36=36--------------ok Hope this helps---ptaylor