Sure, let's analyze each statement one by one to determine whether they are true or false.
### A. An equation to find the cost t, in dollars, of a tetra is [tex]\(8t + 2t + 6 = 37\)[/tex].
This equation does not correctly model the problem given. The correct form of the equation should account for the total number of tetras and the additional cost of the rainbow fish. Hence, the statement is false.
### B. The cost of 4 tetras is the same as the cost of a rainbow fish.
Let [tex]\(t\)[/tex] be the cost of a tetra. A rainbow fish costs [tex]\(t + 6\)[/tex]. For this statement to be true:
[tex]\[ 4t = t + 6 \][/tex]
Solving the equation:
[tex]\[ 3t = 6 \][/tex]
[tex]\[ t = 2 \][/tex]
Thus, 4 tetras would indeed have the same cost as one rainbow fish. This statement is true.
### C. Reducing the number of rainbow fish by 1 would result in a total cost of [tex]$28.50.
Originally, the total cost is given by:
\[ 8t + 2(t + 6) = 37 \]
Let’s find \(t\) by solving this:
\[ 8t + 2t + 12 = 37 \]
\[ 10t + 12 = 37 \]
\[ 10t = 25 \]
\[ t = 2.5 \]
Now, reducing the number of rainbow fish by 1:
\[ 8t + 1(t + 6) = 8(2.5) + 1(2.5 + 6) = 20 + 8.5 = 28.5 \]
So, this statement is true.
### D. One rainbow fish plus 5 tetras cost $[/tex]21.
Using the previously determined cost [tex]\(t = 2.5\)[/tex]:
[tex]\[ 5t + (t + 6) \][/tex]
[tex]\[ 5(2.5) + (2.5 + 6) = 12.5 + 8.5 = 21 \][/tex]
So this statement is also true.
### E. An equation to find the cost r, in dollars, of a rainbow fish is [tex]\(8r + 2(r + 6) = 37\)[/tex].
This equation mistakenly uses [tex]\(r\)[/tex] as the cost of the rainbow fish, which changes the problem context. The correct equation should be set up according to the total number of tetras and the additional cost for the rainbow fish. Thus, this statement is false.
### Conclusion:
Given the analysis, the correct answers are:
- A: False
- B: True
- C: True
- D: True
- E: False
