Question

In a pond, the ratio of newts to frogs was 3:10. 12 more frogs then entered the pond, and the ratio of newts to frogs became 3:11. How many newts are in the pond?

Answer 1

After solving the ratio equations, we find that there are 36 newts in the pond.

Step-by-step explanation:

The question involves finding the quantity of newts in a pond, where the initial ratio of newts to frogs is 3:10. After 12 more frogs enter the pond, the ratio changes to 3:11. To solve this, we can set up two ratio equations based on the given ratios.

Let the number of newts be 3x and the number of frogs be 10x before the additional frogs enter the pond. After 12 more frogs enter, the new ratio becomes:

3x/(10x + 12) = 3/11

By cross-multiplying and solving for x, we get:

11(3x) = 3(10x + 12)

33x = 30x + 36

3x = 36

x = 12

Since there are 3x newts in the pond, we multiply the value of x by 3 to find the number of newts:

Number of newts = 3 * 12 = 36

Therefore, there are 36 newts in the pond.