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.

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): You can put this solution on YOUR website!
This looks like fun
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

RELATED QUESTIONS
The sum of a two-digit number is 6. If the digits are reversed, the new number is 18 less (answered by nyc_function)

The sum of the digits in a two-digit number is 8. When the digits are reversed, the new... (answered by london maths tutor)

The sum of two digits of a two digit number is seven. If the digits are reversed, the new (answered by rapaljer)

A two-digit number is three less than seven times the sum of its digits. If the digits... (answered by 24HoursTutor.com)

A two Digit number is three less than seven times the sum of its digits if the digits are (answered by mananth)

A two digit number is three less than seven times the sum of its digits. if the digits... (answered by stanbon)

Please heeelp. a two-digit number is three less than seven times the sum of its... (answered by josgarithmetic)

the sum of the digits of a two-digit number is 12. if the digits are reversed, the new... (answered by rapaljer)

THE SUM OF THE DIGITS OF A TWO-DIGIT NUMBER IS 12. IF THE DIGITS ARE REVERSED THE NEW... (answered by vleith)