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].
