SOLUTION: a two-digit number is equal to 7 times the units digit. if 18 is added to the number, its digits are reversed. find the number.

Question 186853: a two-digit number is equal to 7 times the units digit. if 18 is added to the number, its digits are reversed. find the number.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let 10x+y=the two digit number
Then 10x+y=7y subtract 7y from each side
10x+y-7y=7y-7y collect like terms
10x-6y=0-------------------------------------eq1
and
10x+y+18=10y+x subtract 10x+y from each side
10x-10x+y-y+18=10y-y+x-10x collect like terms
18=9y-9x or
-9x+9y=18 divide eacn term by 9
-x+y=2-----------------------------------eq2
multiply eq2 by 10 and then add it to eq1 and we get
4y=20 divide each side by 4
y=5 -----------------------------------------the units digit
substitute y=5 into eq2:
-x+5=2 subtract 5 from each side
-x+5-5=2-5 collect like terms
x=3 -------------------------------------------tens digit
The number is
10*3+5=35
CK
35=7*5
35=35
Also
35+18=53
digits are reversed
Hope this helps---ptaylor

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