SOLUTION: A two-digit number is four times the sum of its digits. If its digits are reversed, the new number is 36 more than the original number. What is the original number?

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Question 719778: A two-digit number is four times the sum of its digits. If its digits are reversed, the new number is 36 more than the original number. What is the original number?
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
A two-digit number is four times the sum of its digits.

Let the number be 10x+y and x and y are whole numbers less than or equal to 9.
10x%2By=4%28x%2By%29,
10x%2By=4x%2B4y
6x-3y=0
2x-y=0


If its digits are reversed, the new number is 36 more than the original number.
10y%2Bx=36%2B10x%2By,
10y-y%2Bx-10x=36
-9x%2B9y=36
x-y=-4

SYSTEM TO SOLVE:
highlight%282x-y=0%29
highlight%28x-y=-4%29

Subtract second equation from the first equation. x+0=4, highlight%28x=4%29. Looks like highlight%28y=8%29.