Question 150566
the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digit, the quotient is 6 and the remainder is 8. find the number?
<pre><font size = 4 color = "indigo"><b>
t = tens digit
u = units digit
10t+u = the number
t+u = sum of the digirs

>>...the units digit of a two-digit number 
is 3 less than its tens digit...<<

            {{{u = t - 3}}}

>>...if the number is divided by the sum of 
its digit, the quotient is 6 and the remainder
is 8...<<
                 
              <u> quotient </u>
sum of digits) the number
               __________
               remainder

{{{(quotient)*(sum_of_digits) + (remainder) = (the_number)}}}  

{{{6(t+u)+8 = 10t+u}}}
{{{6t+6u+8=10t+u}}}
{{{-4t+5u=-8}}}

So we have this system of equations:

{{{u = t - 3}}}
{{{-4t+5u=-8}}}

Solve that by substitution and we get

t = 7 and u = 4

So the number is 74.

the units digit, 4, is 3 less than its tens digit 7.  That 
checks.

If the number, 74, is divided by the sum of its digit, 11, 
the quotient is 6 and the remainder is 8

  <u>  6</u>               
11)74
   <u>66</u>
    8

That checks.

Edwin</pre>