A tow digit number is such that the sum of the ones number digit and the tens digit is 10.if the digits are interchanged the new number exceeds the original number by 54.find the number
X+Y=10
10x+y+54=10x+y
you were well on your way, but you second equation makes no sense, since
it would end up as 54 = 0
You should have defined your x and y
In the original number let the unit digit be x and the tens digit by y
So the number was 10y + x
the number reversed would then be
10x + y
So the difference between the new and the old is 54, that is ....
10x + y - (10y + x) = 54
9x - 9y = 54
x - y = 6
add this to the original x + y = 10 to get
2x = 16
x = 8 , then y = 2
the original number, using my definition, was 28
check:
number reversed = 82, and sure enough 82-28 = 54