Question 669208
{{{a}}} = the larger integer
{{{b}}} = the smaller integer
Their sum is 163 translates into {{{a+b=163}}}
When the larger number is divided by the smaller, the quotient is 3 and the remainder is 3 translates into
{{{a=3b+3}}} (If you need it, see the explanation below).
 
You end up with the system
{{{system(a+b=163,a=3b+3)}}}
which can be easily solved by substitution.
Substituting {{{a=3b+3}}} into {{{a+b=163}}} you get
{{{3b+3+b=163}}} <--> {{{4b+3=163}}} <--> {{{4b=163-3}}} <--> {{{4b=160}}} <--> {{{4b/4=160/4}}} <--> {{{highlight(b=40)}}}
Then, substituting {{{b=40}}} into {{{a=3b+3}}} we get
{{{a=3*40+3}}} <--> {{{a=120+3}}} <--> {{{highlight(a=123)}}}
 
EXPLANATION OF WHAT DIVISION, QUOTIENT, AND REMAINDER MEAN:
The quotient is 3.
That means that {{{b}}} fits up to 3 times (but not 4 times) into {{{a}}},
so that {{{3b}}} is no larger than {{{a}}} ({{{3b<=a}}}),
but {{{4b}}} does not fit into {{{a}}}.
It is larger, {{{4b>a}}}
There is a remainder. It is 3.
It turns out that {{{3b<a}}} and the difference is the remainder
{{{a-3b=3}}} <--> {{{a=3b+3}}}