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
I gave a method a few minutes ago.
Price list:
Albacore $12
Barracuda $9
Carp $15
Dogfish $17
Eel $20
Flounder $11
Gar $14
Proof: Call the fish A-G and make all the prices into simple addition equations.
Add all the numbers and equations together. You get:
2(A+B+C+D+E+F+G) = 196.
And thus,
(A+B+C+D+E+F+G) = 98
After that, add together the first, third, fifth, and seventh equations.
(A+B+C+D+E+F+G+A) = 110
And then subtract the last two equations I've written from each other, leaving...
A = 12.
After that, it's a matter of simple addition i know this is late
Thank you Unknown Guy, helped a lot!
To solve this problem, we need to determine the individual cost of each type of fish.
Let's assign variables to the cost of each fish as follows:
- Albacore: A
- Barracuda: B
- Carp: C
- Dogfish: D
- Eel: E
- Flounder: F
- Gar: G
From the given information, we can form the following equations:
1) A + B = 21
2) B + C = 32
3) C + D = 32
4) D + E = 37
5) E + F = 31
6) F + G = 25
7) G + A = 26
To solve these equations, we can use a method called elimination or substitution. In this case, substitution might be simpler. Let's solve these equations step by step using substitution:
From equation 1, we can express A = 21 - B.
Substituting A in equation 7, we get:
G + (21 - B) = 26
G - B = 5
G = B + 5
Substituting A in equation 2, we get:
B + C = 32
(21 - B) + C = 32
C = 11 + B
Substituting C in equation 6, we get:
F + (11 + B) = 25
F + B = 14
F = 14 - B
Substituting F in equation 5, we get:
(14 - B) + E = 31
E = 17 + B
Substituting E in equation 4, we get:
D + (17 + B) = 37
D = 20 - B
Substituting D in equation 3, we get:
C + (20 - B) = 32
C = 12 + B
Now we have expressions for all the variables in terms of B.
Substituting these expressions in equation 7:
(B + 5) + (21 - B) = 26
26 = 26
This shows that our calculations are consistent.
Now let's substitute the expressions back into the original equations to find the values of the variables:
From equation 1, we have:
A + B = 21
(21 - B) + B = 21
21 = 21
From equation 2, we have:
B + C = 32
B + (12 + B) = 32
2B = 20
B = 10
From equation 3, we have:
C + D = 32
(12 + 10) + D = 32
D = 10
From equation 4, we have:
D + E = 37
10 + E = 37
E = 27
From equation 5, we have:
E + F = 31
27 + F = 31
F = 4
From equation 6, we have:
F + G = 25
4 + G = 25
G = 21
From equation 7, we have:
G + A = 26
21 + A = 26
A = 5
Therefore, the individual costs of each type of fish are:
Albacore: $5
Barracuda: $10
Carp: $12
Dogfish: $10
Eel: $27
Flounder: $4
Gar: $21