Question 1004844
Let their ages now be R and M
You are told 
{{{R-7 = 6*(M-7)}}} 
{{{R - 7 = 6M - 42}}}
{{{R = 6M - 35}}}

You are also told
{{{R+1 = 2*(M+1)}}}
{{{R + 1 = 2M + 2}}}
{{{R = 2M + 1}}}

Since R = R, then
{{{6M -35 = 2M + 1}}}
{{{4M = 36}}}
{{{M = 9}}}

If she is 9 then he must be 2*9 + 1  = 19