Question 1099565

<pre>
Adam's father is 19 times as old as Adam. 

F = 19A


Adam's grandfather's age is 14 years less than twice Adam's fathers age. 

G = 2F - 14



The sum of all their ages is 102. 

A + F + G = 102

Solve the system:

{{{system(F=19A,G=2F-14,A+F+G=102)}}}

Substitute (19A) for F in

G = 2F - 14
G = 2(19A) - 14
G = 38A - 14

Substitute (19A) for F and (38A-14) for G in

           A + F + G = 102
A + (19A) + (38A-14) = 102
  A + 19A + 38A - 14 = 102
            58A - 14 = 102
                 58A = 116
                   A = 2

Substitute 2 for A in

F = 19A
F = 19(2)
F = 38

Substitute (38) for F in

G = 2F - 14
G = 2(38) - 14
G = 76-14
G = 62

Edwin</pre>