SOLUTION: The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. Find the original number.

Question 146922: The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. Find the original number.
Found 2 solutions by Nate, ptaylor:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
The number will have digits: xy
~ where x is the tens place, y is the ones place
Number is: 10x + y
The sum of the digits of a two-digit numeral is 8.
x + y = 8
If the digits are reversed, the new number is 18 greater than the original number.
10y + x = 18 + 10x + y
y - x = 2
Now, we have:
x + y = 8
y - x = 2
Substitute using: y - x = 2 or y = 2 + x
x + y = 8
x + 2 + x = 8
2x = 6
x = 3
Substitute again:
y = 2 + x
y = 2 + 3
y = 5
Number is: 10x + y = 10*3 + 5 = 35
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=the tens digit
And let y=the units digit
The original number is 10x+y
If the digits are reversed, the new number is 10y+x
Now we are told the following:
x+y=8--------------------------------------eq1
And
10y+x=10x+y+18-------------------------------eq2
simplifying eq2, by subtracting 10x and also y from each side:
10y-y+x-10x=10x-10x+y-y+18 collect like terms
9y-9x=18 divide each term by -9
x-y=-2------------------------------------------------eq2a
Add eq1 and eq2a:
2x=6 divide each side by 2
x=3-------------------------------the 10's digit
Substitute x=3 into eq1:
3+y=8
y=5------------------------------the units digit
The original number is: 35
The new number is 53 which is 18 greater than 35
Hope this helps---ptaylor

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