Question

A pond contains 20 tadpoles, of which f are frog tadpoles and the others are toad tadpoles. If 10 more frog tadpoles are added to the pond, the probability of catching a frog tadpole is doubled. Find f

Answer 1

By setting up an equation that represents the doubling of the probability of catching a frog tadpole after adding 10 more, we find that there were initially 5 frog tadpoles in the pond.

Step-by-step explanation:

To solve for the number of frog tadpoles initially in the pond (f), we begin by examining the initial conditions. The probability of catching a frog tadpole before the additional 10 are added is f/20. When 10 more frog tadpoles are added, there are (f + 10) frog tadpoles out of 30 total tadpoles. We're told the probability of catching a frog tadpole has doubled, so we set up the equation:

2 × (f/20) = (f + 10)/30

Solving for f gives us the following steps:

1. 2f/20 = (f + 10)/30
2. 60f = 20f + 200 (Multiply both sides by 60 to clear fractions)
3. 60f - 20f = 200
4. 40f = 200
5. f = 5

Thus, there were initially 5 frog tadpoles in the pond.

Answer 2

The value of f is 5

Step-by-step explanation:

Initially, the number of frog tadpoles = f

The initial probability of catching a frog tadpole = f/20

Adding 10 more frog tadpoles,

Number of frog Tadpoles = f +10

Total number of tadpoles in the pond = 20+10 = 30

new probability of catching a frog tadpole = (f+10)/30

New probability of catching a frog tadpole = 2 x Initial probability of catching a frog tadpole

(f+10)/30 = 2 x (f/20)

(f+10)/30 = f/10

f+10 = f x 30/10

f+10 = 3f

2f = 10

f = 5