Posted by joy on .
The sum of the digits of a twodigit number is 16. If the digits are reversed the new number will be 18 greater than the original number. Find the number.

math 
Ms. Sue,
By trial and error, I found that three numbers meet the first criteria: 88, 79, 97.
Which of those numbers meets the second criteria? 
math 
joy,
79

math 
tchrwill,
Let A = the first digit and B + the second digit.
Then A + B = 16 and 10B + A = 10A + B + 18 or B  A = 2
Adding A + B = 16 and B  A = 2 yields B = 9 and A = 7 making the initial number 79.
Therefore, A + B = 16 and 97  79 = 17. 
math 
tchrwill,
Sorry for the mental error. The hand was slower than the eye.
Let A = the first digit and B + the second digit.
Then A + B = 16 and 10B + A = 10A + B + 18 or B  A = 2
Adding A + B = 16 and B  A = 2 yields B = 9 and A = 7 making the initial number 79.
Therefore, A + B = 16 and 97  79 = 18 
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