To determine the number of green fish in the aquarium, let's define two variables:
1. Let [tex]\( g \)[/tex] represent the number of green fish.
2. Let [tex]\( T \)[/tex] represent the total number of fish in the aquarium.
We know from the problem statement that the aquarium has 3 more yellow fish than green fish. Thus, the number of yellow fish can be expressed as [tex]\( g + 3 \)[/tex].
Additionally, it's given that 60 percent of the total fish in the aquarium are yellow. This can be written as:
[tex]\[ 0.6T = \text{number of yellow fish} \][/tex]
Using the information given, we can set up the following equations:
1. The number of yellow fish is equal to [tex]\( g + 3 \)[/tex].
2. The number of yellow fish is also equal to 60 percent of the total number of fish, which can be expressed as [tex]\( 0.6T \)[/tex].
Since both expressions represent the number of yellow fish, we can set them equal to each other:
[tex]\[ g + 3 = 0.6T \][/tex]
Next, we realize that the total number of fish [tex]\( T \)[/tex] is the sum of the number of green fish and the number of yellow fish. Therefore, we can write:
[tex]\[ T = g + (g + 3) \][/tex]
Simplifying this, we get:
[tex]\[ T = 2g + 3 \][/tex]
Now we have two equations:
1. [tex]\( g + 3 = 0.6T \)[/tex]
2. [tex]\( T = 2g + 3 \)[/tex]
We can substitute the second equation into the first equation to eliminate [tex]\( T \)[/tex] and solve for [tex]\( g \)[/tex]:
[tex]\[ g + 3 = 0.6(2g + 3) \][/tex]
Expanding the right-hand side, we get:
[tex]\[ g + 3 = 1.2g + 1.8 \][/tex]
Now, we'll isolate [tex]\( g \)[/tex] on one side of the equation. First, subtract [tex]\( 1.2g \)[/tex] from both sides:
[tex]\[ g - 1.2g + 3 = 1.8 \][/tex]
This simplifies to:
[tex]\[ -0.2g + 3 = 1.8 \][/tex]
Next, subtract 3 from both sides:
[tex]\[ -0.2g = 1.8 - 3 \][/tex]
[tex]\[ -0.2g = -1.2 \][/tex]
Finally, divide both sides by -0.2 to solve for [tex]\( g \)[/tex]:
[tex]\[ g = \frac{-1.2}{-0.2} \][/tex]
[tex]\[ g = 6 \][/tex]
Therefore, the number of green fish in the aquarium is [tex]\( 6 \)[/tex].
