Question 978179
TRIAL AND ERROR:
the current age is a multiple of 8, so we try different multiples of 8.
We can make a table with reasonable ages that are multiples of 8,
and see if the age next year (age+1) would be a multiple of 7.
{{{matrix(3,14,age,8,16,24,32,40,48,56,64,72,80,88,96,104,age+1,9,17,25,32,41,49,57,65,73,81,89,97,105,"7 X __ ?",NO, NO, NO, NO,NO,"YES!",NO,NO, NO, NO, NO, NO,"???!!!")}}}
The age of that person should be {{{highlight(48)}}} this year, and will be {{{49}}} at some time next year.
A person could be {{{104}}} and expect to have another birthday next year,
but it is very rare to be that old,
and someone that old would probably not be asking math question like that one.


MAKING IT LOOK MORE LIKE ALGEBRA:
{{{8n}}}= age this year (for some number {{{n}}} that is a positive integer).
{{{8n+1=7p}}}= age next year (for some number {{{p}}} that is a positive integer).
Let us get some useful relationship from that:
{{{8n+1=7p}}}
{{{7n+n+1=7p}}}
{{{n+1=7p-7n}}}
{{{n+1=7(p-n)}}}
We know that {{{n+1}}} is a positive integer, so {{{p-n}}} must be a positive integer too.
{{{p-n=1}}} gives us {{{n+1=7}}}--->{{{n=7-1}}}--->{{{n=6}}} and since {{{age=8n}}} ,
{{{system(age=8n,n=6)}}}--->{{{system(age=8n,8n=8*6)}}}--->{{{highlight(age=48)}}}
{{{p-n>=2}}} gives us {{{n+1>=14}}}--->{{{n>=14-1}}}--->{{{n>=13}}} and since {{{age=8n}}} ,
{{{system(age=8n,n>=13)}}}--->{{{system(age=8n,8n>=8*13)}}}--->{{{age>=104}}} ,
which not a very reasonable answer, as it is unlikely to reach age 104
while expecting to live until the next year and the next birthday,
and asking this kind of math question.
However, if I am in good physical and mental health 40 years from now,
I will post the same question and cackle with glee.

FOR A TRICK QUESTION
I do not think it is meant to be a trick question, so I would answer the answer above.
For a trick question,
that person could have had a birthday and turned {{{56}}} earlier this yea.
So, at the beginning of next year would still be {{{56}}} (until the next birthday.
As {{{56=8*7}}} is a multiple of {{{8}}} and a multiple of {{{8}}} ,
that person's age would be {{{56}}}= a multiple of {{{8}}} now,
and {{{56}}}= a multiple of {{{7}}} for some time next year,
at the beginning of the year, before the next birthday,