Question 166678: When the digits of a two-digit number are reversed, the new nwmber is 9 more than the original number, and the sum of the digits of the original number is 11.What is the original number?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! When the digits of a two-digit number are reversed, the new number is 9 more
than the original number, and the sum of the digits of the original number
is 11. What is the original number?
:
Write the two digit number as: (10x + y); where x=10's digit and y=units digit
:
"When the digits of a two-digit number are reversed, the new number is 9 more than the original number,"
(10y+x) = (10x+y) + 9
10y - y = 10x - x + 9
9y = 9x + 9
Simplify, divide equation by 9
y = x + 1
:
and the sum of the digits of the original number is 11.
x + y = 11
:
What is the original number?
:
Substitute (x+1) for y in the above equation
x + (x+1) = 11
2x = 11 - 1
2x = 10
x = 5, then obviously y = 6
;
The number is: 56
:
:
Check solution in the statement:
"When the digits of a two-digit number are reversed, the new number is 9 more than the original number,"
65 = 56 + 9
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