Question

The number of ducks in a pond is equal to the square root of the number of fish, and the number of turtles is equal to the cube root of the number of fish. The number of fish in the pond is more than 1 but less than 100. There are no fractional or negative numbers of ducks, fish, or turtles.

There are____fish,___ ducks, and___turtles in the pond.

Answer 1

ANSWER:

Fishes = 64, ducks = 8 and turtles = 4

STEP-BY-STEP EXPLANATION:

Given that the number of ducks in a pond is equal to the square root of the number of fish, and the number of turtles is equal to the cube root of the number of fish.

→ Number of ducks = √(Number of fishes)

→ Number of turtles = ³√(Number of fishes)

So, we can say that the number of fishes must be square root or cube root of a number lies between 1 and 100.

And the number of fish in the pond is more than 1 but less than 100.

We need to find out the number of fishes, ducks and turtles in the pond. (There are no fractional or negative numbers of ducks, fish, or turtles.)

Now,

Of 2: ³√8 ≠ whole number

Of 3: ³√27 ≠ whole number

Of 4: ³√64 = 4 which is a whole number

Therefore,

Number of ducks = √(Number of fishes)

8 = √64

Number of turtles = ³√(Number of fishes)

4 = ³√64

Hence, there are 64 fishes, 8 ducks and 4 turtles.