Question 1134846

let Kawika’s age be {{{K}}} and Tony’s age {{{T}}}

if the ratio of Kawika’s age to Tony’s age is {{{3:4}}}, we have
{{{K/T=3/4}}}....solve for {{{T}}}
{{{4K=3T}}}
{{{T=4K/3}}}.......eq.1

Two years ago, 
Kawika’s age was {{{K-2}}} and Tony’s age was {{{T-2}}}

if their average age was {{{12}}} years, we have

{{{(K-2+T-2)/2=12}}} 
{{{K+T-4=12*2}}} 
{{{K+T=24+4}}} 
{{{K+T=28}}} ....solve for {{{T}}}
{{{T=28-K}}}.......eq.1

from eq.1 and eq.2 we have

{{{4K/3=28-K}}}
{{{4K=84-3K}}}
{{{4K+3K=84}}}
{{{7K=84}}}
{{{K=84/7}}}
{{{K=12}}}

 answer:  Kawika is {{{12}}} years old now.

{{{T=28-K}}}->{{{T=28-12}}}->{{{T=16}}}

check the ratio: 

{{{12/16=3/4}}}->{{{cross(12)3/cross(16)4=3/4}}}->{{{3/4=3/4}}}->true