Question 724360
{{{a}}} = tens digit
{{{b}}} = units digit
so the value of the number is {{{10a+b}}} and
the sum of the digits is {{{a+b}}}
The tens digit is 5 more than the units digit translates as
{{{a=b+5}}}
 
Now comes the hard part:
If "the number" is divided by the sum of its digits, the partial quotient is 7 and the remainder is 6 translates as
{{{10a+b=7(a+b)+6}}} (dividend = divisor x quotient + remainder)
 
Another way to see that:
The number divided by {{{a+b}}} is 7 plus the fraction that we get when we divide the remainder by {{{a+b}}}
{{{(10a+b)/(a+b)=7+6/(a+b)}}}
Multiplying times {{{a+b}}} both sides of the equal sign we get {{{10a+b=7(a+b)+6}}}
 
Anyway,
{{{10a+b=7(a+b)+6}}} --> {{{10a+b=7a+7b+6}}} --> {{{3a+b=7b+6}}} --> {{{3a=6b+6}}} --> {{{3a/3=(6b+6)/3}}} --> {{{a=2b+2}}}
Now we have a system of linear equations:
{{{system(a=b+5,a=2b+2)}}} --> {{{2b+2=b+5}}} --> {{{b+2=5}}} --> {{{b=5-2}}} --> {{{highlight(b=3)}}}
{{{system(a=b+5,b=3)}}} --> {{{a=3+5}}} --> {{{highlight(a=8)}}}