Answer:
38
Step-by-step explanation:
Let the six knights be represented by the variables A, B, C, D, E and F. (A figure is attached.)
We know the neighbors of A, F and B, sum to 20; this gives us
B+F = 20
The neighbors of B, A and C, sum to 28:
A+C = 28
The neighbors of C, B and D, sum to 36:
B+D = 36
The neighbors of D, C and E, sum to 44:
C+E = 44
The neighbors of E, D and F, sum to 52:
D+F = 52
The neighbors of F, E and A, sum to 60:
E+A = 60
We are concerned with the number of peanuts the knight who counted 52 has. The one with a sum of 52 is the one whose neighbors are D and F, which is knight E.
We will use the equations with the variable E. First we use
E+A = 60
Subtract A from each side:
E+A-A = 60-A
E = 60-A
Substitute this into the other equation with E:
C+E = 44
C+60-A = 44
Subtract 60 from each side:
C+60-A-60 = 44-60
C-A = -16
The other equation we have with C and A is
A+C = 28
This gives us the system
-A+C = -16
A+C = 28
We will eliminate A by adding the two equations:
-A+A+C+C = -16+28
2C = 12
Divide both sides by 2:
2C/2 = 12/2
C = 6
Substitute this into
C+E = 44
6+E = 44
Subtract 6 from each side:
6+E-6 = 44-6
E = 38
Knight E had 38 peanuts.
