SOLUTION: The product of the digits of a two-digit number is one third of that number.If we add 18 to the required number , we get a number consisting of the same digits written in reverse o

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Question 1061522: The product of the digits of a two-digit number is one third of that number.If we add 18 to the required number , we get a number consisting of the same digits written in reverse order. Find the number.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
10t%2Bu, Number.

The description is transcribable into system%28t%2Au=%2810t%2Bu%29%2F3%2C%2810t%2Bu%29%2B18=10u%2Bt%29.

Solve the system for t and u, the TENS place and the ONES place digits.

Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
Answer. 24. The number is 24.

Solution 

From the second condition, you momentarily have 


(10u+t) - (10t+u) = 18,   or

9u - 9t = 18,   or

u - t = 2.


Hence, the two-digit numbers to check are 13, 24, 35, . . . (and it is clear that the numbers are not so big). 
In addition, only few of them are multiples of 3.


Then you find the answer 24 by trial and error much faster than by solving the quadratic equation.

For many other problems on reversing digits in 2-digit integers see the lesson
    - Word problems on interchanging digits of numbers
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Miscellaneous word problems".