SOLUTION: Using the five step method answer the following: When the digits of a two-digit number are reversed, the new number is 9 more than the orginal number, and the sum of the digits of

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Question 176873: Using the five step method answer the following: When the digits of a two-digit number are reversed, the new number is 9 more than the orginal number, and the sum of the digits of the orginal number is ll. what is the orginal number?
Found 2 solutions by Mathtut, MathTherapy:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let a and b be the digits of our number. remember our two digit number ab can be written as 10a+b and the reversed number ba can be written as 10b+a
:
a+b=11................eq 1
(10b+a)=(10a+b)+9.....eq 2
:
rewrite eq 1 to a=11-b and plug that value into eq 2
:
10b+11-b=10(11-b)+b+9
:
9b+11=110-10b+b+9
:
9b+11=-9b+119
:
18b=108
:
highlight%28b=6%29
:
a=11-b=11-6=5%29
:
so our number is highlight%2856%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Let f = 1st digit, and s = second digit
Then the original number is 10(f) + s, or 10f + s
When reversed, the new number will be 10(s) + f, or 10s + f
Since when reversed, the new number (10s + f) is 9 more than original number (10f + s), then 10s + f – 9 = 10f + s = 9s -9f = 9, or s – f = 1
Since the sum of the original digits is 11, then s + f = 11
We then get:
s - f = 1
s + f = 11
2s = 12
s = 6
Therefore, 6 – f = 1
f = 5
The original number is 56.