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Question 8 (Essay Worth 10 points)
(04.04 MC)
The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Write and solve a rational equation. Show your work.



Answer :

GinnyAnswer
To determine the number of blue fish in the aquarium, follow these steps:

1. Define the Variables:
- Let [tex]\( b \)[/tex] represent the number of blue fish in the aquarium.
- Since there are 10 more red fish than blue fish, the number of red fish can be represented as [tex]\( b + 10 \)[/tex].

2. Formulate the Total Number of Fish:
- The total number of fish in the aquarium is the sum of blue fish and red fish:
[tex]\[ b + (b + 10) = 2b + 10 \][/tex]

3. Express the Percentage Relationship:
- It's given that 60% of the total number of fish are red. So, we can set up the following equation to represent this relationship:
[tex]\[ 0.6 \times (2b + 10) = b + 10 \][/tex]

4. Solve the Equation:
- Distribute the 0.6 on the left side of the equation:
[tex]\[ 0.6 \times 2b + 0.6 \times 10 = b + 10 \][/tex]
[tex]\[ 1.2b + 6 = b + 10 \][/tex]
- Isolate [tex]\( b \)[/tex] by subtracting [tex]\( b \)[/tex] from both sides of the equation:
[tex]\[ 1.2b - b + 6 = 10 \][/tex]
[tex]\[ 0.2b + 6 = 10 \][/tex]
- Subtract 6 from both sides:
[tex]\[ 0.2b = 4 \][/tex]
- Divide both sides by 0.2:
[tex]\[ b = \frac{4}{0.2} \][/tex]
[tex]\[ b = 20 \][/tex]

5. Conclusion:
- The number of blue fish in the aquarium is [tex]\( \boxed{20} \)[/tex].

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