Question

On an island, the frogs are either green or blue. The number of blue frogs increases by 60%, and the number of green frogs decreases by 60%. This has the effect that the new ratio of the number of blue frogs to the number of green frogs matches the original ratio of the number of green frogs to the number of blue frogs. By what percentage has the total number of frogs changed?

(a) 10% decrease
(b) 20% decrease
(c) 30% decrease
(d) 40% decrease

Answer 1

The total number of frogs has doubled, resulting in a 100% increase.

Step-by-step explanation:

To determine the percentage change in the total number of frogs, we need to find the difference between the initial and final number of frogs, and then divide it by the initial number of frogs. Let's assume that initially, there are 'g' green frogs and 'b' blue frogs. After the increase in blue frogs and decrease in green frogs, the new ratio of blue frogs to green frogs is the same as the original ratio of green frogs to blue frogs. Therefore, we have:

blue frogs / green frogs = g / b

After increasing the blue frogs by 60% and decreasing the green frogs by 60%, we get:

(b + 0.6b) / (g - 0.6g) = g / b

Simplifying this equation, we have:

1.6b / 0.4g = g / b

Cross multiplying, we get:

1.6b^2 = 0.4g^2

Simplifying further:

b^2 = (0.4/1.6)g^2

b^2 = 0.25g^2

Taking the square root, we have:

b = 0.5g

Substituting this value in the equation (b + g) / (b + g) * 100, we can find the percentage change in the total number of frogs:

(0.5g + g) / (0.5g + g) * 100

=(1.5g) / (1.5g) * 100

= 100%

Therefore, the total number of frogs has increased by 100% or doubled in size.