SOLUTION: 15. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 27 less than the original number. Find the original number.

Question 96059This question is from textbook
: 15. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 27 less than the original number. Find the original number. This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the 10's digit and y = the units digit:
:
just write what it says:
"The sum of the digits of a two-digit number is 11."
x + y = 11
and
y = (11 - x); can use for substitution
:
"If the digits are reversed, the new number is 27 less than the original number.
Original number: 10x + y
Reversed number: 10y + x
:
Then the equation would be:
(10y + x) = 10x + y - 27
10y - y + x - 10x = -27
9y - 9x = -27
Simplify, divide equation by 9
y - x = -3
:
Substitute (11-x) for y in the above equation
(11 - x) - x = -3
-2x = - 3 - 11
-2x = -14
x = -14/-2
x = +7 is the 10's digit
:
11 - 7 = 4 is the units digit
:
Check solutions
74 - 47 = 27
:

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