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?

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)   (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:

.

Now, simplify it:

.

Simplify it one more time:

.

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)   (Show Source): You can put this solution on YOUR website!
The number is and the description directly translated into a system is
.

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

System can be restated .

72-----small mental mis-step when I solved the simple two-variable system.
Correct result IS 27.
Answer by MathTherapy(10552)   (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:
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