If $a$, $b$, and $c$ are integers satisfying $a + \frac 1b = \frac{22}{7}$, $b + \frac 1c = 8$, and $abc = 21$, then find $c + \frac 1a$.

a=1;p=0; b=1;c=1;n=a+1/b;m=b+1/c;r=a*b*c;if(n==22/7 and m==8 and r==21, goto loop, goto next);loop:p=p+1;printp," =",a,b,c;next:a++;if(a<100, goto4,0);a=1;b++;if(b<100, goto4, 0);a=1;b=1;c++;if(c<100, goto4,0)

 

OUTPUT:  a = 3,  b =7,  c =1

c + 1 /a ==1 + 1/3 =4 / 3  or  1 1/3