SOLUTION: The tens digit of a certain two digit number is two more than the units digit. The original number is 18 more than the number formed by interchanging the digits. What is the origin

Question 551139: The tens digit of a certain two digit number is two more than the units digit. The original number is 18 more than the number formed by interchanging the digits. What is the original number? Please help me solve this!!!!
Found 2 solutions by mathstutor458, richwmiller:
Answer by mathstutor458(57) (Show Source): You can put this solution on YOUR website!
let the number = xy
The tens digit of a certain two digit number is two more than the units digit.
so,x=y+2
The original number is 18 more than the number formed by interchanging the digits.
xy=yx+18
from this we can understand that x,y values must be even numbers and x value is greater than y value.
take y=2,so x=2+2=4 (because no odd numbers)
xy=42
check xy=yx+18
=>42=24+18
=>42=42 satisfies the equations
so the original number is 42.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x=2+y
10x+y=18+10y+x which reduces to
y=x-2 which is equivalent to x=2+y
so any x (tens digit) that is 2 more than y (units digit) will work
97=79+18
86=68+18
75=57+18
64=46+18
53=35+18
42=24+18
31=13+18

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