SOLUTION: The sum of the digits of a two digit number is 9. If the digits are reversed, the resulting number is 45 more than the original. What is the number?

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Question 1011629: The sum of the digits of a two digit number is 9. If the digits are reversed, the resulting number is 45 more than the original. What is the number?
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let  a  and  b are the digits of your number  n,  so that  n = 10a + b.

The number after interchanging digits is  10b + a.

Then you have the system of two equations for the unknowns  a  and  b:

system%28a%2Bb+=+9%2C%0D%0A%0D%0A%2810b+%2Ba%29+-+%2810a+%2B+b%29+=+45%29.

Now,  simplify it:

system+%28a%2Bb=+9%2C%0D%0A%0D%0A9b+-+9a+=+45%29.

Simplify it one more time:

system+%28a%2Bb=+9%2C%0D%0A%0D%0Ab+-+a+=+5%29.

Solve it.

The solution is   b=7,  a=2.

Hence,  the number is  10a + b = 10*2+7 = 27.

Answer.  27.

For more problems of this type see the lesson Word problems on interchanging digits of numbers in this site.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The number is 10t%2Bu and the description directly translated into a system is
system%28t%2Bu=9%2C%2810u%2Bt%29-%2810t%2Bu%29=45%29.

Simplifying the second equation relating the reversal,
10u-u+t-10t=45
9u-9t=45
u-t=5

System can be restated system%28u%2Bt=9%2Cu-t=5%29.



72-----small mental mis-step when I solved the simple two-variable system.
Correct result IS 27.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the digits of a two digit number is 9. If the digits are reversed, the resulting number is 45 more than the original. What is the number?
Number: highlight_green%2827%29