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The ratio of goldfish to angelfish in an aquarium was 3:5. The total number of goldfish and angelfish was 32. (a) Find the number of goldfish in the aquarium. (b)When some angelfish were added into the aquarium, the ratio of goldfish to angelfish became 4: 9.Find the number of angelfish that were added into the aquarium.​

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Answer:

Explanation:

a. Find the number of goldfish in the aquarium.

The ratio of goldfish to angelfish in the aquarium is 3:5, which means that there are 3 parts goldfish for every 5 parts angelfish. If the total number of goldfish and angelfish is 32, then there are 3/8 * 32 = 12 goldfish in the aquarium.

b. When some angelfish were added into the aquarium, the ratio of goldfish to angelfish became 4: 9. Find the number of angelfish that were added into the aquarium.

The new ratio of goldfish to angelfish is 4:9, which means that there are 4 parts goldfish for every 9 parts angelfish. If we let x be the number of angelfish that were added to the aquarium, then the number of angelfish in the aquarium is 5 + x. The total number of goldfish and angelfish in the aquarium is still 32, so we have the equation:

12 + x = 4/9 * (5 + x)

Solving for x, we get x = 8. Therefore, 8 angelfish were added to the aquarium.

Here is the summarized solution:

a. Number of goldfish in the aquarium: 12

b. Number of angelfish added to the aquarium: 8

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