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Question 118384: The sum of two digits is 8. If the digits of the number are reversed, the number formed is 36 more than the number. What is the number?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=the tens digit
And y=the units digit
(Note: We know that this number is 10x+y. Like, for example, 45 could be written at 10*4+5. We also know that if the digits are reversed, the number formed would be 10y+x)
Now we are told that:
x+y=8--------------------------------eq1
And we are also told that:
10y+x=10x+y+36-------------------------eq2
In eq1, subtract y from both sides and we get
x+y-y=8-y or
x=8-y ---------------------------------------eq1a
Now substitute x=8-y into eq2
10y+8-y=10(8-y)+y+36 get rid of parens
10y+8-y=80-10y+y+36 collect like terms on each side
9y+8=116-9y subtract 8 from and add 9y to both sides
9y+9y+8-8=116-8-9y+9y collect like terms
18y=108 divide both sides by 18
y=6 -----------------------------------------the units digit
substitute y=2 into eq1a
x=8-6=2------------------------------------the 10's digit
original number is 26
CK
6+2=8
8=8
also
62=26+36
62=62
Hope this helps---ptaylor
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