SOLUTION: I need help with this one question is there anyone out there that is willing to help me? The sum of the digits of a certain two-digit number is 12. Reversing its digits decreases

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Question 929228: I need help with this one question is there anyone out there that is willing to help me?
The sum of the digits of a certain two-digit number is 12. Reversing its digits decreases the number by 18. What is the number...
Please us elimination of substitution. If not that's okay. Please show me your work:)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = one's digit in original number
Let y = ten's digit in original number
value of original number = 10y+%2B+x
In new number (with reversed digits):
y = one's digit
x = ten's digit
value of new number = 10x+%2B+y
given: The sum of the digits of a certain two-digit number is 12. Reversing its digits decreases the number by 18.
We can now form these equations:
"Sum of digits of two-digit no. is 12" (original number)
y+%2B+x+=+12...eq.1
"Reverse the digits, the no. is decreased by 18."
10y+%2B+x+-+18+=+10x+%2B+y
10y+-+y+%2B+x+-18+=+10x+%2B+y+-+y
9y+%2B+x+-18+=+10x
9y+%2B+x+-+x+-18+=+10x+-+x
9y+-18=+9x
9y%2F9+-18%2F9+=+9x%2F9
y+-2=+x....eq.2
Now compare the two equations:
y+%2B+x+=+12
y+-2=+x
We can substitute %28y+-2%29 for x in the first equation to solve:
y+%2B+%28y+-2%29+=+12
2y+-2=+12
2y+%2B+2+-+2+=+12+%2B2
2y+=+14
2y%2F2+=+14%2F2
highlight%28y+=7%29
Now substitute this value for y into one of the equations to find x:
y+-2+=+x
7-2+=+x
highlight%28x+=+5%29
Our original number is 10y+%2B+x=highlight%2875%29.