SOLUTION: A number of two digits is increased by 45 when the digits are reversed. The sum of the two digits is 9. find the number

Question 709239: A number of two digits is increased by 45 when the digits are reversed. The sum of the two digits is 9. find the number
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
The Setup
Equation 1: (The sum of the digits is 9)
Equation 2: (The number is increased by 45 when the digits are reversed)
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Solution
Solve equation 1 for one of the variables. I will solve for A.
Equation 1:

Now plug (9-B) into equation 2 for A.
Equation 2:

Multiply the 10 through.

Combine like terms.

Add 9B to both sides.

Subtract 9 from both sides.

Divide both sides by 18.

Now solve for A, while using 7 for B.
{From earlier in the problem)

The number was 27.
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