SOLUTION: Explain how to answer this by elimination using multiplication please: The sum of the digits of a two digit number is 11. If the digits are reversed, the new number is 45 more tha

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Question 568218: Explain how to answer this by elimination using multiplication please:
The sum of the digits of a two digit number is 11. If the digits are reversed, the new number is 45 more than the original number. Find the number and show your work.
Found 2 solutions by mananth, issacodegard:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
let the digits be x & y x in the tens place and y in the units place
x+y=11
The number is 10x+y
reversed
10y+x
10y+x= 10x+y +45
9y-9x=45
/9
y-x=5
x+y =11
y-x=5
add the two equations
2y=16
/2
x=8
if x = 8 then y= 3
the number is 83
m.ananth@hotmail.ca

Answer by issacodegard(60) (Show Source):
You can put this solution on YOUR website!
Let the number be N and let its digits be x (tens) and y (ones). Then,

We can create two equations from what's given,

So,

Multiply the 1st eqn by 9 and add it to the second to get,

Divide the second by 9 to get y=8. Then, we have

So,

So, the original number was 38.