SOLUTION: The sum of the digits of a certain two digit number is 7. The reversing digit increase the number by 9

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Question 309420: The sum of the digits of a certain two digit number is 7. The reversing digit increase the number by 9
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Set-Up:
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Equation 1: A+%2B+B+=+7
Equation 2: 10A+%2B+B+%2B+9+=+A+%2B+10B
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Solution:
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Solve equation 1 for one of the variables
I solved for B
Equation 1: A+%2B+B+=+7
B+=+7+-+A
Now plug (7 - A) into equation 2 for B
Equation 2: 10A+%2B+B+%2B+9+=+A+%2B+10B
10A+%2B+%287+-+A%29+%2B+9+=+A+%2B+10%2A%287+-+A%29 Simplify
10A+%2B+7+-+A+%2B+9+=+A+%2B+70+-+10A Simplify
9A+%2B+16+=+70+-+9A Add 9A to both sides
18A+%2B+16+=+70 Subtract 16 from both sides
18A+=+54 Divide both sides by 18
highlight%28A+=+3%29
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Now plug 3 into equation 1 for A
B+=+7+-+A
B+=+7+-+3
highlight_green%28B+=+4%29