"Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more than the tetras. She paid a total of $37. Which of the following are true ? Select all that apply ;
A. The cost of 4 tetras is the same as the cost of a rainbow fish.
B. One rainbow fish plus 5 tetras Cost $21.
C. An equation to find the cost r, in dollars of a rainbow fish is 8r + 2(r + 6) = 37
D. Reducing the number of rainbow fish by 1 would result in a total cost of $28.50
E. An equation to find the cost t, in dollars , of a tetra is 8t + 2t + 6 = 37

The correct answer is: Statements B & D are true for the given situation

"Step-by-step solution:-
Let the cost of each Tetras be '$x' and that of each rainbow fish be '$y'.
Now, as per the given condition-
cost of rainbow fish = 6 + cost of tetras
∴ y = 6 + x
∴ -x + y = 6 …........................................ (Taking all the variables on LHS)
∴ x - y = -6 ........................................... (Multiplying both sides by -1) .......................................... (Equation i)
Also, we know that-
Total amount paid = Cost of tetras + Cost of rainbow fish
∴ Total amount paid = number of tetras × price per tetra + number of rainbow fish × price per rainbow fish
∴ 37 = 8x + 2y ........................................ (From given information)
i.e 8x + 2y = 37 ........................................................................................................................................... (Equation ii)
Adding 2× Equation i & Equation ii, we get-
2x - 2y = -12
+ 8x + 2y = 37
10x + 0 = 25
∴ 10x = 25
∴ x = 25/10
∴ x = 2.5
Substituting x = 2.5 in Equation i, we get-
x - y = -6
∴ 2.5 - y = - 6
∴ 2.5 + 6 = y ............................... (Taking all constants on LHS)
∴ 8.5 = y
"A. The cost of 4 tetras is the same as the cost of a rainbow fish.
Cost of 4 tetras = Cost of a rainbow fish
∴ 4x = y
∴ 4 × 2.5 = 8.5
∴ 20 ≠ 8.5
Since, LHS ≠ RHS for the given statement, it is False.
B. One rainbow fish plus 5 tetras Cost $21.
Cost of 1 rainbow fish + Cost of 5 tetras = 21
∴ 8.5 + 5(2.5) = 21
∴ 8.5 + 12.5 = 21
∴ 21 = 21
Since, LHS = RHS for the given statement, it is True.
C. An equation to find the cost r, in dollars of a rainbow fish is 8r + 2(r + 6) = 37
8r + 2(r + 6) = 37
∴ 8r + 2r + 12 = 37
∴ 8r + 2r = 37 - 12 ................................................ (Taking all the constants together)
∴ 10r = 25
∴ r = 25/10 ................................................. (Dividing both sides by 10)
∴ r = 2.5 ≠ 8.5
Since the cost of 1 rainbow fish = 2.5 as per the given statement and as per our solution, cost of a rainbow fish = y = 8.5, the given statement is False.
D. Reducing the number of rainbow fish by 1 would result in a total cost of $28.50
Total cost for 1 less rainbow fish = total cost - cost of 1 rainbow fish
∴ 28.5 = 37 - x ..................... (As per given information)
∴ 28.5 = 37 - 8.5 ................ (From Equation i)
∴ 28.5 = 28.5
Since, LHS = RHS for the given statement, it is True.
"E. An equation to find the cost t, in dollars , of a tetra is 8t + 2t + 6 = 37
8t + 2t + 6 = 37
∴ 8t + 2t = 37 - 6 ….............................................. (Taking all the constants together)
∴ 10t = 31
∴ t = 31/10 ............................................... (Dividing both sides by 10)
∴ t = 3.1 ≠ 2.5
Since the cost of 1 tetras = 3.1 as per the given statement and as per our solution, cost of a tetras = x = 2.5, the given statement is False.
Final Answer:-
∴ Statements B & D are true for the given situation.

Let's talk about the cost equation.
A company must determine the cost of producing and selling one of its products to create a cost equation. It must also calculate the overhead costs of production. Typically, the cost equation is the cost of manufacturing and selling one item multiplied by the number of items sold and added to the company's overhead costs.
For example, a company with $300,000 in overhead costs that manufacture and sells products that cost the company $5 each has a cost equation of 300,000 + $5. (5 x number of products sold).