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.

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(2198) (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

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