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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
The Setup
Equation 1: A+%2B+B+=+9 (The sum of the digits is 9)
Equation 2: 10A+%2B+B+%2B+45+=+A+%2B+10B (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: A+%2B+B+=+9
A+=+9+-+B
Now plug (9-B) into equation 2 for A.
Equation 2: 10A+%2B+B+%2B+45+=+A+%2B+10B
10%289-B%29+%2B+B+%2B+45+=+%289-B%29+%2B+10B
Multiply the 10 through.
90+-+10B+%2B+B+%2B+45+=+9+-+B+%2B+10B
Combine like terms.
135+-+9B+=+9+%2B+9B
Add 9B to both sides.
135+=+9+%2B+18B
Subtract 9 from both sides.
126+=+18B
Divide both sides by 18.
highlight%287+=+B%29
Now solve for A, while using 7 for B.
A+=+9+-+B {From earlier in the problem)
A+=+9+-+%287%29
highlight_green%28A+=+2%29
The number was 27.