Question 951408
Let the fraction be {{{X/Y}}}
{{{(X+5)/(Y+5)=4/7}}}
{{{4(Y+5)=7(X+5)}}}
{{{4Y+20=7X+35}}}
1.{{{-7X+4Y=15}}}
.
.
{{{(X-1)/(Y-1)=2/5}}}
{{{5(X-1)=2(Y-1)}}}
{{{5X-5=2Y-2}}}
2.{{{5X-2Y=3}}}
Multiply eq. 2 by 2 and add to eq. 1,
{{{-7X+4Y+10X-4Y=15+6}}}
{{{3X=21}}}
{{{X=7}}}
So then,
{{{5(7)-2Y=3}}}
{{{35-2Y=3}}}
{{{-2Y=-32}}}
{{{Y=16}}}