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

To determine the cost of each individual fish, we can set up a system of equations using the given prices. By solving this system of equations, we can find the cost of each fish.

Step-by-step explanation:

To solve this problem, we can set up a system of equations using the given information.

Let's assign variables to each fish: Albacore = A, Barracuda = B, Carp = C, Dogfish = D, Eel = E, Flounder = F, Gar = G.

We can create the following equations based on the given prices:

A + B = 21

B + C = 24

C + D = 32

D + E = 37

E + F = 31

F + G = 25

G + A = 26

Next, we can solve this system of equations using the method of substitution or elimination. By substituting values from one equation into another, we can gradually solve for the cost of each fish:

A = 26 - G

D = 37 - E

C = 32 - D

B = 24 - C

A = 21 - B

Now, we can substitute the values of B, C, D, and E into the equations for A and D to find their respective costs:

A = 26 - G

D = 37 - (31 - E)

By simplifying and solving these equations, we can find the costs of each fish. The values of A, B, C, D, E, F, and G represent the cost of each fish respectively.

Answer 2

See below

Step-by-step explanation:

Let the following symbols stand for the cost of each fish type:

A = Albacore

B = Baracuda

C = Carp

D = Dogfish

E = Eel

F = Flounder

G = Gar

---------------

We are told the following (numbers are in $):

A+B = 21

B+C = 24

C+D = 32

D+E = 37

E+F = 31

F+G = 25

G+A = 26

I count 7 unknowns (A,B,C,D,E,F,G) and 7 equations. In principle, the answers should therefore be possible [it can be a little tedious]. I'll rewrite each expression so that only one variable remains on the left side:

A = 21 - B

B = 24 - C

C = 32 - D

D = 37 - E

E = 31 - F

F = 25 - G

G = 26 - A

====

Now find combinations of these expressions that will allow us to (slowly) remove one of the two unknowns.

=====

A = 21 - B

A = 21 - (24 - C)

A = C - 3

A = (32 - D) - 3

A = 29 - D

A = 29 - (37 - E)

A = E - 8

A = (31 - F) - 8

A = 23 - F

A = 23 - (25 - G)

A = G - 2

A = (26 - A) - 2

2A = 24

A = 12 We found one price. Albacore cost $12 each.

=====

Now use A = 12 to find B

A = 21 - B

12 = 21 - B

B = 9 Barracuda cost $9 each

And so on:

B+C = 24

9+C = 24

C = 15 Carp are $15 each

C+D = 32

15+D = 32

D = 17 Dogfish are $17 each

D+E = 37

17+E = 37

E = 20 Eels are $20 each [Not worth it]

E+F = 31

20+F = 31

F = 11 Flounder are $11 each

F = 25 - G

11 = 25 - G

G = 14 Gar are $14 each

Wheh. I'm going fishing.