SOLUTION: Please Help Me To Answer this The sum of a digit of a two digit number is 10 if the digits are reversed the number increased by 36. What is the original Number? PLEASE Help Me T

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Question 929114: Please Help Me To Answer this
The sum of a digit of a two digit number is 10 if the digits are reversed the number increased by 36. What is the original Number?
PLEASE Help Me To Answer
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
We can now form these equations:
"Sum of digits of two-digit no. is 10" (original number)
y+%2B+x+=+10...eq.1
"Reverse the digits, the no. is increased by 36."
10y+%2B+x+%2B+36+=+10x+%2B+y
10y+-+y+%2B+x+%2B+36+=+10x+%2B+y+-+y
9y+%2B+x+%2B+36+=+10x
9y+%2B+x+-+x+%2B+36+=+10x+-+x
9y+%2B+36+=+9x
9y%2F9+%2B+36%2F9+=+9x%2F9
y+%2B+4=+x....eq.2
Now compare the two equations:
y+%2B+x+=+10
y+%2B+4+=+x
We can substitute %28y+%2B+4%29 for x in the first equation to solve:
y+%2B+%28y+%2B+4%29+=+10
2y+%2B+4=+10
2y+%2B+4+-+4+=+10+-+4
2y+=+6
2y%2F2+=+6%2F2
highlight%28y+=+3%29
Now substitute this value for y into one of the equations to find x:
y+%2B+4+=+x
3+%2B+4+=+x
highlight%28x+=+7%29
Our original number is highlight%2837%29.