Question 1024431
WITH TWO VARIABLES:
{{{t}}}= tens' digit (so {{{1<=t<=9}}} and {{{t}}} is an integer)
{{{u}}}= units' digit (so {{{0<=u<=9}}} and {{{u}}} is an integer)
 
The problem says that "the units' digit is twice the tens' digit,"
so {{{u=2t}}} , which means {{{u>t}}} , since {{{t>=1}}} .
The problem also says that "the difference between the digits in a two-digit numeral is 3."
That means that
{{{u-t=3}}} .
 
So we could say that we are going to solve the system og linear equations
{{{system(u=2t,u-t=3)}}} by substitution,
meaning that we will substitute the expression {{{2t}}} for {{{u}}} in {{{u-t=3}}} .
We get {{{2t-t=3}}}-->{{{t=3}}} ,
and substituting {{{3}}} for {{{t}}} in {{{u=2t}}} , we get
{{{u=2-3}}}-->{{{u=6}}} .
So, {{{system(t=3,u=6)}}}, and the number is {{{highlight(36)}}} .
 
WITH ONE VARIABLE:
{{{t}}}= the tens' digit.
So the units digit, which is "twice the tens' digit", is {{{2t}}} ,
and the difference between the digits is {{{2t-t}}} ,
which according to the problem is {{{3}}} .
Our equation is {{{2t-t=3}}} , which simplifies to {{{t=3}}} .
So {{{t=3}}} is the tens' digit;
{{{2t=2*3=6}}} is the units digit,
and the number is {{{highlight(36)}}} .
 
GUESS AND CHECK METHOD:
The tens' digit cannot be {{{0}}} , because then the number would not really be "a two-digit numeral".
 
The tens' digit cannot be {{{4}}} , because then "the units" digit" would have to be {{{3*4=12}}} , which is not a digit.
For the same reason, the tens' digit cannot be more than {{{4}}} .
So, the tens' digit must be {{{1}}} , {{{2}} , or {{{3}}} .
 
If the tens' digit were {{{1}}} , the units' digit would be {{{2*1=2}}} ,
and the two-digit numeral would be {{{12}}} ,
but the difference between the digits would be {{{2-1=1}}} ,
so {{{12}}} is not the two-digit numeral.
 
If the tens' digit were {{{2}}} , the units' digit would be {{{2*2=4}}} ,
and the two-digit numeral would be {{{24}}} ,
but the difference between the digits would be {{{4-2=2}}} ,
so {{{24}}} is not the two-digit numeral.
 
If the tens' digit were {{{3}}} , the units' digit would be {{{2*3=6}}} ;
the two-digit numeral would be {{{36}}} ,
and the difference between the digits would be {{{6-3=3}}} , as the problem says
so {{{highlight(36)}}} is the two-digit numeral.