Question

В одном городе 20 % семей, имеющих кошек, имеют также и собак, 25 % семей, имеющих собак, имеют также и кошек, а 20 % всех семей не имеют ни кошек, ни собак. Сколько семей в этом городе имеют и кошек, и собак?

Answer 1

Analysis and Solution

To solve this problem, we can use a system of equations. Let's denote the total number of families in the city as T, the number of families with cats as C, and the number of families with dogs as D.

From the given information, we can create the following equations:

1. 20% of families with cats also have dogs: 0.2C = D 2. 25% of families with dogs also have cats: 0.25D = C 3. 20% of all families have neither cats nor dogs: 0.2T = (T - C - D)

We can solve this system of equations to find the values of C and D.

Solving the System of Equations

Let's solve the system of equations step by step:

From equation 1, we have 0.2C = D. We can rewrite this equation as C = 5D.

Substituting this value of C into equation 2, we get 0.25D = 5D.

Simplifying, we find D = 0.25 / 5 = 0.05.

Substituting this value of D back into equation 1, we find C = 5 * 0.05 = 0.25.

Now, we can substitute the values of C and D into equation 3 to find T:

0.2T = (T - 0.25 - 0.05)

Simplifying, we get 0.2T = T - 0.3.

Rearranging the equation, we find 0.8T = 0.3.

Dividing both sides by 0.8, we get T = 0.3 / 0.8 = 0.375.

Answer

Therefore, there are 0.25 families in the city that have both cats and dogs.

To summarize: - Number of families with cats (C) = 0.25 - Number of families with dogs (D) = 0.05

Please note that the values of C, D, and T are given as percentages, so we need to convert them to actual numbers by multiplying by the total number of families in the city.

Let me know if there's anything else I can help you with!