SOLUTION: Witch two digit number when multiplied by three the answer will be the opposite way like 12*3=21

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Witch two digit number when multiplied by three the answer will be the opposite way like 12*3=21       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 758272: Witch two digit number when multiplied by three the answer will be the opposite way like 12*3=21
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If there was a 2-digit number that multiplied times 3 yielded a 2-digit number with the same digits, but reversed, we would be able to get the solution as follows.
a = tens digit in the original number
b = ones digit in the original number
value of the original number = 10a%2Bb
value of the reversed number = 10b%2Ba
three times the original number = 3%2810a%2Bb%29
We are looking for digits a and b that satisfy the equation
3%2810a%2Bb%29=10b%2Ba
a and b are digits in our base 10 numbering system, so they must belong in the set
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
3%2810a%2Bb%29=10b%2Ba --> 30a%2B3b=10b%2Ba --> 30a-a=10b-3b --> 29a=7b
Since 29a=7b is a multiple of 29,then 7b is the same multiple of 29.
Since 7 is not a multiple of 29, then b should be a multiple of 29.
Since the only digit that could be called a multiple of 29 is 0, we would have b=0 with a=0 as the only possible solution, but 00 is not what I would call a 2-digit number.