Question

question 8 (mc) (essay worth 10 points) the aquarium has 3 more yellow fish than green fish. 60 percent of the fish are yellow. how many green fish are in the aquarium? write and solve a rational equation. show your work.

Explanation:

Step1: Define Variables

Let \( g \) be the number of green fish. Then the number of yellow fish is \( g + 3 \). The total number of fish is \( g+(g + 3)=2g + 3 \).

Step2: Set Up Rational Equation

We know that 60% of the fish are yellow, so the number of yellow fish is also \( 0.6(2g + 3) \). Since the number of yellow fish is \( g + 3 \), we can set up the equation:

$$ \frac{g + 3}{2g + 3}=0.6 $$

Step3: Solve the Equation

Multiply both sides by \( 2g + 3 \) (assuming \( 2g+3
eq0 \), which is true for positive \( g \)):

$$ g + 3=0.6(2g + 3) $$

Expand the right - hand side:

$$ g + 3 = 1.2g+1.8 $$

Subtract \( g \) from both sides:

$$ 3=0.2g + 1.8 $$

Subtract 1.8 from both sides:

$$ 0.2g=3 - 1.8=1.2 $$

Divide both sides by 0.2:

$$ g=\frac{1.2}{0.2}=6 $$

Answer:

The number of green fish in the aquarium is 6.