Question

An aquarium contained an equal number of horseshoe crabs and sea stars. After 15 horseshoe crabs were removed and 27 sea stars were removed, the ratio of horseshoe crabs to sea stars was 5:3. How many horseshoe crabs and sea stars were there at first? Solve this problem and explain your reasoning.

Answer 1

There were initially 45 horseshoe crabs and 45 sea stars in the aquarium.

Step-by-step explanation:

Let's first represent the initial number of horseshoe crabs as x and the initial number of sea stars as x.

After 15 horseshoe crabs and 27 sea stars were removed, the new ratio is 5:3. This means that the new number of horseshoe crabs is x - 15 and the new number of sea stars is x - 27.

We can set up the following equation to represent the ratio:

1. (x - 15)/(x - 27) = 5/3

Cross-multiply to solve for x:

1. 3(x - 15) = 5(x - 27)
2. 3x - 45 = 5x - 135
3. -2x = -90
4. x = 45

Therefore, there were initially 45 horseshoe crabs and 45 sea stars in the aquarium.

Answer 2

45 horseshoe crabs and 45 sea stars

Step-by-step explanation:

The aquarium initially contained x crabs and x sea stars.

"After 15 horseshoe crabs and 27 sea stars are removed the ratio of horseshoe crabs to sea stars is 5:3"

(x-15):(x-27) = 5:3

(x-15)/(x-27) = 5/3

3(x-15) = 5(x-27)

3x-45 = 5x-135

90 = 2x

x = 45