SOLUTION: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number formed is 27 more than the original number. Find the original number.

Question 158853: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number formed is 27 more than the original number. Find the original number.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 7. When the digits are reversed, the number formed is 27 more than the original number. Find the original number.
.
Let x = ones digit
and y = tens digit
.
from: "The sum of the digits of a two-digit number is 7."
x+y =7 (equation 1)
.
from: "When the digits are reversed, the number formed is 27 more than the original number."
10x + y = (10y + x) + 27
9x = 9y + 27
x = y + 3 (equation 2)
.
Solve equation 1 for y:
x+y =7
y =7-x
.
Substitute the above into equation 2 and solve for x:
x = y + 3
x = 7-x + 3
2x = 7+3
2x = 10
x = 5 (ones digit)
.
Subsitute the above into equation 1 and solve for y:
x+y =7
5+y =7
y = 7-5
y = 2
.
Solution: The original number is 27
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