Question

В пруду плавали 25 гусей и несколько уток. когда к пруду подошли ещё 15 гусей, то всех гусей стало в 5 раз больше чем уток. сколько было уток? Вычисли ответ задачи двумя способами.

Answer 1

25+15=40
40:5=8
Ответ в пруду плавали 8 уток

Answer 2

Problem Analysis

Let's analyze the problem step by step:

1. Initially, there were 25 geese and some ducks in the pond. 2. When 15 more geese approached the pond, the number of geese became 5 times greater than the number of ducks.

We need to find the number of ducks in the pond.

Solution 1: Using Algebra

Let's assume the number of ducks in the pond is x.

According to the problem, the number of geese initially was 25, and the number of ducks was x.

When 15 more geese approached the pond, the number of geese became 5 times greater than the number of ducks. This can be expressed as:

25 + 15 = 5x

Simplifying the equation:

40 = 5x

Dividing both sides by 5:

8 = x

Therefore, there were 8 ducks in the pond.

Solution 2: Using Ratio

We can also solve the problem using ratios.

Initially, the ratio of geese to ducks was 25:x.

When 15 more geese approached the pond, the ratio became 5:1.

We can set up the following proportion:

25/x + 15 = 5/1

Cross-multiplying:

25 + 15x = 5x

Simplifying the equation:

15x - 5x = 25

10x = 25

Dividing both sides by 10:

x = 2.5

Since the number of ducks cannot be a decimal, we can conclude that there was an error in the problem or the information provided.

Therefore, the number of ducks in the pond cannot be determined accurately based on the given information.

Please note that the second solution assumes that the number of geese and ducks are whole numbers. If the number of ducks can be a decimal, then the solution would be 2.5.

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