The tetras and goldfishes Anna bought is an illustration of a system of simultaneous equations. The solution to the system of equations shows that options (c) and (e) are true
To do this, we use the following representation:
[tex]t \to[/tex] Tetra
[tex]r \to[/tex] Rainbow Fish
The $37 spent on the fishes means:
[tex]8t + 2r = 37[/tex]
1 rainbow fish cost $6 more means:
[tex]r = 6 + t[/tex]
Substitute [tex]r = 6 + t[/tex] in [tex]8t + 2r = 37[/tex]
[tex]8t + 2(6 + t)=37[/tex]
Open bracket
[tex]8t + 12 + 2t=37[/tex]
Collect like terms
[tex]8t + 2t = 37-12[/tex]
[tex]10t = 25[/tex]
Solve for t
[tex]t = 2.5[/tex]
Solve for r
[tex]r = 6 + t[/tex]
[tex]r = 6 +2.5[/tex]
[tex]r = 8.5[/tex]
Testing the options, we have:
Option (a) and (d) are incorrect because the possible equations are:
[tex]8t + 2t + 6 = 37[/tex] and [tex]8t + 2(6 + t)=37[/tex]
Option (b)
The cost of 4 tetras is 4t
[tex]4t = 4 * 2.5 = 10[/tex]
The cost of 1 rainbow fish is r
[tex]r = 8.5[/tex]
Both values are not equal. So, (b) is incorrect
Option (c)
When the number of rainbow fish is reduced by 1, the expression becomes
[tex]8t + r[/tex]
And the value is:
[tex]8t + r = 8 \times 2.5+8.5[/tex]
[tex]8t + r = 28.5[/tex]
Option (c) is correct
Option (e)
1 rainbow fish and 5 tetras is represented as:
[tex]r + 5t[/tex]
The value is:
[tex]r + 5t = 8.5 + 5 \times 2.5[/tex]
[tex]r + 5t = 21[/tex]
Option (e) is correct
Based on the above computations, we can conclude that options (c) and (e) are true
Read more about equations at:
https://brainly.com/question/16763389
