Question

Пожалуйста помогите) В пруду водится три вида рыб: окуни, щуки и карпы. Когда у рыбака спросили, сколько он сегодня поймал, он ответил:«Окуней в 3 раза больше, чем остальной рыбы»;«Щук в 4 раза меньше, чем остальной рыбы».Сколько процентов от всего улова составляют карпы?​

Answer 1

Введем обозначения. Пусть рыбак поймал А окуней, С щук и К карпов.

Тогда, по условию получим систему::

$\begin{cases} A=3(C+K)\\ 4C=A+K\end{cases}$

Подставим во второе уравнение соотношение для А:

$4C=3(C+K)+K$

$4C=3C+3K+K$

$\boxed{C=4K}$

Подставим в первое уравнение соотношение для С:

$A=3(4K+K)$

$A=3\cdot5K$

$\boxed{A=15K}$

Зная выражения для А и С через K, найдем требуемое отношение:

$\dfrac{K}{A+C+K} =\dfrac{K}{15K+4K+K} =\dfrac{K}{20K} =\dfrac{1}{20} =5\%$

Ответ: 5 %

Answer 2

Problem Analysis

The fisherman caught three types of fish: perch, pike, and carp. He mentioned that he caught three times more perch than the other fish and four times fewer pike than the other fish. We need to determine the percentage of the total catch that carp represents.

Solution

Let's assume that the number of carp caught is represented by C, the number of perch caught is represented by P, and the number of pike caught is represented by K.

Based on the information given, we can write the following equations:

1. P = 3*(P + K) - The number of perch caught is three times more than the sum of the number of perch and pike caught.

2. K = (P + K)/4 - The number of pike caught is four times fewer than the sum of the number of perch and pike caught.

We can solve these equations to find the values of P and K and then calculate the percentage of the total catch represented by carp.

Solution Steps

1. Substitute equation 2 into equation 1 to eliminate K: - P = 3*((P + K)/4 + K) - Simplifying the equation: - P = 3*(P/4 + K/4 + K) - P = 3*(P/4 + 5K/4) - P = 3P/4 + 15K/4

2. Move all terms with P to one side of the equation: - P - 3P/4 = 15K/4 - 4P/4 - 3P/4 = 15K/4 - P/4 = 15K/4

3. Multiply both sides of the equation by 4 to eliminate the fractions: - 4*(P/4) = 4*(15K/4) - P = 15K

4. Substitute the value of P in equation 2 to find K: - K = (P + K)/4 - K = (15K + K)/4 - K = 16K/4 - 4K = 16K - 3K = 0 - K = 0

5. Substitute the value of K in equation 1 to find P: - P = 3*(P + K) - P = 3*(P + 0) - P = 3P - 2P = 0 - P = 0

6. Calculate the percentage of the total catch represented by carp: - Percentage of carp = (C / (P + K + C)) * 100 - Percentage of carp = (C / (0 + 0 + C)) * 100 - Percentage of carp = (C / C) * 100 - Percentage of carp = 100%

Therefore, carp represents 100% of the total catch.

Answer

Carp represents 100% of the total catch.