SOLUTION: THE SUM OF THE DIGITS OF THE TWO DIGITS- NUMBER IS 12.If the order of the digits is reversed,the resulting number is 18 more than the original number.FIND THE ORIGINAL NUMBER.
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Question 475317: THE SUM OF THE DIGITS OF THE TWO DIGITS- NUMBER IS 12.If the order of the digits is reversed,the resulting number is 18 more than the original number.FIND THE ORIGINAL NUMBER.
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
Let the 2-digit number be AB, where A is in the ten's place and B is in the one's place.
The value of AB is 10*A + B
If you reverse the order to BA then the value is 10*B + A
Set up equations:
We know the sum of A and B is 12. We know the value of BA is 18 more than value of AB.
Combine like terms in 2nd equation
Subtract B on both sides, Subtract A on both sides
Divide by 9 on both sides
Now substitute A+2 for B in 1st equation:
Subtract 2 on both sides
Divide by 2 on both sides
B = A + 2 = 5+2 = 7
Therefore the original number (AB) is 57
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