SOLUTION: in a two digit number two times the ten digit is eight less than seven times the one"s digit.when the digits are interchanged, it reduces by nine.find the number?

Question 687054: in a two digit number two times the ten digit is eight less than seven times the one"s digit.when the digits are interchanged, it reduces by nine.find the number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let x = the 10's digit
let y = the one's digit
then
10x+y = the number
:
in a two digit number two times the ten digit is eight less than seven times the one"s digit.
2x = 7y - 8
2x - 7y = -8
:
when the digits are interchanged, it reduces by nine.
10y + x = 10x + y - 9
10y - y + x - 10x = -9
9y - 9x = -9
Divide by -9
x - y = 1
x = y + 1
:
In the 1st equation replace x with (y+1)
2(y+1) - 7y = -8
2y + 2 - 7y = -8
-5y = -8 - 2
-5y = -10
y = +2
:
Find x using x = y + 1
x = 2 + 1
x = 3
therefore
32 is the number
:
:
Check this in the statement:
"when the digits are interchanged, it reduces by nine"
23 = 32 - 9

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