SOLUTION: The sum of the digits of a 2-digit number is 8.The number obtained by interchanging the digits exceeds the given number by 18. Find the given number

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Question 700041: The sum of the digits of a 2-digit number is 8.The number obtained by interchanging the digits exceeds the given number by 18. Find the given number
Answer by Stitch(470) (Show Source):
You can put this solution on YOUR website!
The set up is tricky for this problem.
Let A equal one of the numbers
Let B equal one of the numbers
A & B are one digit numbers so they are positive but less than 10
Equation 1:
Equation 2:
The numbers are multiplied by 10 to put them in the tens place.
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Solve equation 1 for one of the variables
Equation 1:

Now plug (8 - B) into equation 2 for A
Equation 2:

Simplify

Combine like terms

Add 9B to both sides

Subtract 8 from both sides

Divide both sides by 18

Now go back and use 5 for B and solve for A.