Question 148582
Let Alex's age now be a. Let Percy's age be p
In three years, Alex will be a+3 and Percy will be p+3
Last year, Alex was a-1 and Percy was p-1

You are told that in 3 years Alex will be 3 times as old as Percy
{{{a+3 = 3(p+3)}}}
{{{a+3 = 3p + 9}}}
{{{a - 3p = 6}}}
You are also told that last year Alex was 7 times older than Percy
{{{a-1 = 7(p-1)}}}
{{{a-1 = 7p - 7}}}
{{{a - 7p = -6}}}

Now you can use substitution or elimination to solve. We'll use elimination here
{{{a - 3p = 6}}}
{{{a - 7p = -6}}}  Subtract the second equation from the first {{{-a+7p = 6}}}
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{{{0a + 4p = 12}}}
{{{4p = 12}}}
{{{p = 3}}}

Percy is 3 now. 
So that makes Alex {{{a - 3p = 6}}}
{{{a - 3*4 = 6}}}
{{{a - 9 = 6 }}}
{{{a = 15}}}
Alex is 15.

Check your answers.
is 15-1 = 7*2 check
is 15+3 = 3(3+3) check