SOLUTION: The sum of the digits of a two-digit number is 16. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
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Question 248060: The sum of the digits of a two-digit number is 16. If the digits are reversed, the new number is 18 less than the original number. Find the original number. Answer by richwmiller(17219) (Show Source):
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Let a and b be the digits of a number
a+b=16
a=16-b
10(a)+b-10b-(a)=18
substitute b-16 for a
10(16-b)+b-10b-(16-b)=18
160-10b+b-10b-16+b=18
160-16-18=18b
160-34=18b
126=18b
7=b
9=a
9+7=16
original number 97
new number 79
97-79=18
