SOLUTION: The sum of the digits of a two-digit number is 8. The number obtained by interchanging the two digits exceeds the given number by 36. Find the number.

Question 653770: The sum of the digits of a two-digit number is 8. The number obtained by interchanging the two digits exceeds the given number by 36. 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 units
then
10x+y = the two digit number
:
Write an equation for each statement
:
The sum of the digits of a two-digit number is 8
x + y = 8
:
The number obtained by interchanging the two digits exceeds the given number
by 36.
interchanged = original + 36
10y + x = 10x + y + 36
Combine like terms on the left:
10y - y - 10x + x = 36
9y - 9x = 36
simplify, divide by 9
y - x = 4
:
Use elimination with the 1st equation
y - x = 4
y + x = 8
-----------adding eliminates x, find y
2y = 12
y = 6
You can finish this problem now I am sure

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