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Question 91492: A number is 6 times the sum of its digits. The tens digit is 1 greater than the units digit. Find the number.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=the tens digit
And let y=the units digit
Then the number (N)=10x+y
Now we are told that:
10x+y=6(x+y)-----------------------eq1
We are also told that:
x=y+1-------------------eq2
Lets simplify eq1:
10x+y=6(x+y) get rid of parens
10x+y=6x+6y subtract y and also 6x from both sides
10x+y-y-6x=6x-6x+6y-y collect like terms
4x=5y divide both sides by 4
x=(5/4)y-------------------------eq1
substitute x=(5/4)y into eq2 and we get
(5/4)y=y+1 multiply both sides by 4
5y=4y+4 subtract 4y from both sides
5y-4y=4
y=4------------------the unit digit
substitute y=4 into eq1:
x=(5/4)*4=20/4=5-----------------------the tens digit
The number =10x+y=10*5+4=54---------the number
CK
sum of digits is 5+4=9
54=6*9
the tens digit,5, is 1 greater than the unit digit 4
Hope this helps---ptaylor
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