Question 1138228
<br>
a = Edwin
b = his father
c = his grandfather<br>
(1) Edwin, his father, and his grandfather have an average age of 53.<br>
{{{(a+b+c)/3 = 53}}}<br>
(2) One-half of his grandfather's age, plus one-third of his father's age, plus one-fourth of Edwin's age is 65.<br>
{{{c/2+b/3+a/4 = 65}}}<br>
(3) 4 years ago, Edwin's grandfather was four times as old as Edwin.<br>
{{{c-4 = 4(a-4)}}} -->  {{{c = 4a-12}}}<br>
Equation (3) gives you one equation in a and c; so eliminate b between equations (1) and (2) to give you a second equation in a and c.<br>
From (1): {{{a+b+c = 159}}}
From (2): {{{3c/2+b+3a/4 = 195}}}
Subtracting: {{{c/2-a/4 = 36}}}<br>
Substitute (3) into this last equation:<br>
{{{(2a-6)-a/4 = 36}}}
{{{7a/4-6 = 36}}}
{{{7a/4 = 42}}}
{{{7a = 42*4}}}
{{{a = 6*4 = 24}}}<br>
So Edwin is 24.<br>
4 years ago, Edwin was 20; his grandfather then was 4 times as old, so he was 80.  So now the grandfather's age is 80+4 = 84.<br>
The sum of Edwin's age and his grandfather's age is 24+84 = 108, and the sum of all three ages is 159, so Edwin's father's age is 159-108 = 51.<br>
ANSWER: Edwin is 24; his father is 51; his grandfather is 84.<br>
To check, verify that equation (2) is satisfied:<br>
{{{84/2+51/3+24/4 = 42+17+6 = 65}}}