Help with math problem? I know the answer just not how to do it?

Question

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 $24
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 a flounder for $31
You can buy a flounder and a gar for $25
You can buy a gar and an albacore for $26
Determine the cost of each individual fish

Answer 1

a + b= $21
b + c =$24
c + d =$32
d + e =$37
e + f =$31
f + g =$25
g + a= $26

I would say just do
trial & error because they're all different
variables and there is no possible way you can
linear combination or subsitution for them.

Answer 2

This is a system of equations. I'll just use the first letter for each fish.
a + b = 21
b + c = 24
c + d = 32
d + e = 37
e + f = 31
f + g = 25
g + a = 26

Now solve for g in the last equation and substitute upwards in the list of equations.
g + a = 26 ---> g = 26 - a
f + (26 - a) = 25 ---> f = a - 1
e + (a - 1) = 31 ---> e = 32 - a
d + (32 - a) = 37 ---> d = a + 5
c + (a + 5) = 32 ---> c = 27 - a
b + (27 - a) = 24 ---> b = a - 3
a + (a - 3) = 21 ---> 2a = 24 ---> a = 12

Now that you know a is $12, you can go back and find all the others easy enuff.

Answer 3

#1 a + b = 21
#2 b + c = 24
#3 c + d = 32
#4 d + e = 37
#5 e + f = 31
#6 f + g = 25
#7 g + a = 26
#8 a - c = -3 (subtracting #2 from #1)
#9 a + d = 29 (add #3 and #8)
#10 a - e = -8 (#9 - #4)
#11 a + f = 23 (#10 + #5)
#12 a - g = -2 (#11 - #6)
#13 2a = 24 (#12 + #7)
a = 12
b = 9
c = 15
d = 17
e = 20
f = 11
g = 14