Question 1024431: v the units' digit is twice the tens' digit. Find the numeral.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! WITH TWO VARIABLES:
 = tens' digit (so  and is an integer)
 = units' digit (so  and is an integer)
The problem says that "the units' digit is twice the tens' digit,"
so  , which means  , since  .
The problem also says that "the difference between the digits in a two-digit numeral is 3."
That means that
 .
So we could say that we are going to solve the system og linear equations
 by substitution,
meaning that we will substitute the expression  for in .
We get  --> ,
and substituting  for in , we get
 --> .
So,  , and the number is  .
WITH ONE VARIABLE:
= the tens' digit.
So the units digit, which is "twice the tens' digit", is ,
and the difference between the digits is  ,
which according to the problem is .
Our equation is , which simplifies to .
So is the tens' digit;
 is the units digit,
and the number is .
GUESS AND CHECK METHOD:
The tens' digit cannot be  , because then the number would not really be "a two-digit numeral".
The tens' digit cannot be  , because then "the units" digit" would have to be  , which is not a digit.
For the same reason, the tens' digit cannot be more than .
So, the tens' digit must be  ,  .
If the tens' digit were , the units' digit would be  ,
and the two-digit numeral would be  ,
but the difference between the digits would be  ,
so is not the two-digit numeral.
If the tens' digit were  , the units' digit would be  ,
and the two-digit numeral would be  ,
but the difference between the digits would be  ,
so is not the two-digit numeral.
If the tens' digit were , the units' digit would be  ;
the two-digit numeral would be  ,
and the difference between the digits would be  , as the problem says
so is the two-digit numeral.
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