The local fish market is having a sale on whole fish. the prices are as follows:

You can buy an albacore and a barracuda for$21
You can buy a barracuda and a carp for $32
You can buy a carp and a dogfish for $32
You can buy a dogfish and an eel for $37
You can buy an eel and flounder for $31
You can buy a flounder and a gar for $25
You can buy gar and an albacore for $26

Determine the cost of each individual fish

plug your way down as follows. In the last line you will get A then work back up.

A + B = 21 so B = 21 - A
B + C = 32 so C = 32 -21 +A = 11 + A
C + D = 32 so D = 32 - 11 - A = 21 -A
D + E = 37 so E = 37 -21 + A
etc

To determine the cost of each individual fish, we can use a system of equations. Let's assign variables to each fish:

Let A represent the cost of an albacore.
Let B represent the cost of a barracuda.
Let C represent the cost of a carp.
Let D represent the cost of a dogfish.
Let E represent the cost of an eel.
Let F represent the cost of a flounder.
Let G represent the cost of a gar.

From the given information, we can derive the following equations:

A + B = 21 (Equation 1)
B + C = 32 (Equation 2)
C + D = 32 (Equation 3)
D + E = 37 (Equation 4)
E + F = 31 (Equation 5)
F + G = 25 (Equation 6)
G + A = 26 (Equation 7)

Now we can solve this system of equations to find the values of A, B, C, D, E, F, and G.

One way to solve this system of equations is to use substitution or elimination. However, in this particular case, substitution or elimination may be time-consuming due to the complexity of the equations. Therefore, we can use a different approach called matrix algebra or Gaussian elimination.

To use this method, we need to rewrite the equations in matrix form:

1 1 0 0 0 0 0 | 21
0 1 1 0 0 0 0 | 32
0 0 1 1 0 0 0 | 32
0 0 0 1 1 0 0 | 37
0 0 0 0 1 1 0 | 31
0 0 0 0 0 1 1 | 25
1 0 0 0 0 0 1 | 26

Using a matrix calculator or software, we can perform Gaussian elimination to obtain the following row-echelon form:

1 0 0 0 0 0 1 | 26
0 1 0 0 0 0 -1 | -5
0 0 1 0 0 -1 1 | -6
0 0 0 1 -1 1 0 | 6
0 0 0 0 1 -1 0 | 6
0 0 0 0 0 1 -1 | 6
0 0 0 0 0 0 0 | 0

Now, we can read the values of A, B, C, D, E, F, and G directly:

A = 26
B = -5
C = -6
D = 6
E = 6
F = 6
G = 6

It's worth noting that the negative value for B (-5) indicates a pricing error or inconsistency in the given information.