SOLUTION: a two digit number is such that twice the tens digit added to eleven times the units digit is equal to the number itself. find the number.

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Question 961329: a two digit number is such that twice the tens digit added to eleven times the units digit is equal to the number itself. find the number.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
t= the tens digit.
u= the units digit.
For each digit/variable, there are only 10 choices (0, or 1, or 2, or ..., or 8, or 9).

10t%2Bu= the value of the number (the number itself),
just like the value of 48 is 10%2A4%2B8=40%2B8=48 , and
just like the value of 72 is 10%2A7%2B2=70%2B2=72 .

2t=twice the tens digit
11u= eleven times the units digit
2t%2B11u= twice the tens digit added to eleven times the units digit

"Twice the tens digit added to eleven times the units digit is equal to the number itself" means that
2t%2B11u=10t%2Bu .

Solving:
2t%2B11u=10t%2Bu--->2t%2B11u-u=10t%2Bu-u--->2t%2B10u=10t--->2t%2B10u-2t=10t-2t--->10u=8t--->10u%2F2=8t%2F2--->5u=4t

5u is obviously a multiple of 5 ,
so 4t must be a multiple of 5 too.
That means that t must be a multiple of 5 ,
and being a digit (from 0 to 9), the only choice is
highlight%28t=5%29 .
Then, 4t=4%2A5--->4t=20 ,
and system%285u=4t%2C4t=20%29 means that 5u=20--->u=20%2F5--->highlight%28u=4%29 .
So the number is highlight%2854%29 , of course.