Question 608861
Juan's age = J
Suki's age = S

J={{{1/2}}}S because Juan is one half as old as Suki.

Also J+8={{{3/4}}}(S+8) because in 8 years Juan will be {{{3/4}}} as old as Suki.

SO

J+8={{{3/4}}}S+({{{3/4}}})8

J+8={{{3/4}}}S+6
subtract 8 from both sides of the equation
J={{{3/4}}}S-2
Since J={{{1/2}}}S then
{{{1/2}}}S={{{3/4}}}S-2
Subtract {{{3/4}}}S from both sides 
-{{{1/4}}}S=-2
Multiply both sides by -4
S=8 and Juan is {{{1/2}}}8 or 4