The aquarium has 1 fewer red fish than blue fish. 60 percent of the fish are blue. How many blue fish are in the aquarium? Write and solve a rational equation. Show your work.

Answer 1

To solve this problem, let's first define the variables we'll use:

Let \( b \) be the number of blue fish and \( r \) be the number of red fish.

According to the problem:

1. There is 1 fewer red fish than blue fish, which can be expressed as: \[ r = b - 1 \]

2. We also know that 60% of the total fish are blue. The total number of fish can be defined as: \[ \text{Total fish} = b + r \]

Now we can substitute the expression for \( r \) into the equation for the total number of fish: \[ \text{Total fish} = b + (b - 1) = 2b - 1 \]

Since 60% of the total fish are blue, we can set up the following equation: \[ b = 0.6 \times (2b - 1) \]

Now we can simplify and solve this equation. First, distribute 0.6: \[ b = 1.2b - 0.6 \]

Next, we'll move all terms involving \( b \) to one side: \[ b - 1.2b = -0.6 \] \[ -0.2b = -0.6 \]

Now, divide both sides by -0.2: \[ b = \frac{-0.6}{-0.2} = 3 \]

Thus, the number of blue fish in the aquarium is: \[ \boxed{3} \]

To verify the solution, we can find the number of red fish: \[ r = b - 1 = 3 - 1 = 2 \]

Now, let's calculate the total number of fish: \[ \text{Total fish} = b + r = 3 + 2 = 5 \]

Finally, we check if 60% of the total fish are indeed blue: \[ 0.6 \times 5 = 3 \]

Since 3 is the number of blue fish, our solution is confirmed to be correct, and the number of blue fish in the aquarium is \( \boxed{3} \).