Question 972441
<pre>
The other tutor is technically correct because he interpreted "the difference
of the digits" as "the first digit minus the second digit".  However I think
your teacher meant the ABSOLUTE DIFFERENCE, "larger minus smaller", rather
than "first-second", as "difference" is usually taken.  This shows a difficulty
in semantics that we run into in mathematics.

The tens digit = t
The units digits = u
The two-digit number = (10t+u)
The number obtained by reversed = (10u+t)
</pre>
Seven times a two digit number is equal to four times the number obtained by reversing  the digits. 
<pre>
Replace the words "a two digit number" by (10t+u)
Replace the words "the number obtained by reversing the digits" by (10u+t). 
Then the above sentence becomes
</pre>
Seven times (10t+u) is equal to four times (10u+t).
<pre>
Replace the words "Seven times" by "7*"
Replace the words "four times" by "4*" 
Replace the words "is equal to" by "=":

7(10t+u) = 4*(10u+t)

Simplify:

70t+7u = 40u+4t
   66t = 33u
Divide both sides by 33
    2t = u
</pre>
>>...the difference  between  the two  digits  is 3,...<<
<pre>
I am interpreting this as ABSOLUTE difference.  So we have to make sure 
that we take the smaller digit away from the larger digit.  We can tell
by 2t = u that the units digit u is larger because it equals twice what 
the tens digit equals. so

LARGER DIGIT - SMALLER DIGIT = 3

                       u - t = 3

So we have the system of equations:

{{{system(2t=u,u-t=3)}}}

From the first equation, we substitute 2t for u in the second equation:

 u-t = 3
2t-t = 3
   t = 3

Substitute in either equation of the system:

  2t = u
2(3) = u
   6 = u

Since the tens digit is t=3 and the units digit is u=6,
the number is 36

Checking:
</pre>
Seven times a two digit number, 36, which gives 7×36=252

is equal to four times the number obtained by reversing the digits, 63,
which gives 4×63 = 252.
<pre>
That checks.
</pre>
the (ABSOLUTE) difference between the two digits is 3, 6-3 = 3,
<pre>
So it checks.

Edwin</pre>