A =  ( 

) 
while to get the value 2, take the above matrix and interchange the first two columns. Thus the values the determinant of A can take are precisely 0, ±1, ±2.
ax + (10  a)y  =  35  
bx + (16  b)y  =  35  
cx + (26  c)y  =  35 
 

  = 0. 
Remember that a, b, c are positive integers, a < 10, b < 16, c < 26. Also x > y > 0. By inspection, we must have a = 9, b = 8 and c = 9. This yields x = 15/4 and y = 5/4. Thus the cost of a chicken before noon is $15/4, and the cost after noon is $5/4.