Question

Наташа Маша Оля собрали открытки Наташа Собрала в 2 раза больше чем Оля Маша Собрала в 4 раз больше чем Аня всего они собрали 168 открыток Сколько собрал открыток каждый из них

Answer 1

Наташа 2х
Маша 4х
Оля 1 х
2+4+1=7
168÷7=24
24-Оля
24×2=48 Наташа
24×4=96Маша

Answer 2

Problem Analysis

We are given that Natasha, Masha, and Olya collected a total of 168 postcards. Natasha collected twice as many postcards as Olya, and Masha collected four times as many postcards as Anya. We need to determine how many postcards each person collected.

Solution

Let's assign variables to represent the number of postcards collected by each person: - Let N represent the number of postcards collected by Natasha. - Let M represent the number of postcards collected by Masha. - Let O represent the number of postcards collected by Olya. - Let A represent the number of postcards collected by Anya.

From the given information, we can write the following equations: 1. Natasha collected twice as many postcards as Olya: N = 2O. 2. Masha collected four times as many postcards as Anya: M = 4A. 3. The total number of postcards collected is 168: N + M + O + A = 168.

We can now solve these equations to find the values of N, M, O, and A.

Solving the Equations

Substituting the value of N from equation 1 into equation 3, we get: 2O + M + O + A = 168.

Simplifying the equation, we have: 3O + M + A = 168.

Substituting the value of M from equation 2 into the simplified equation, we get: 3O + 4A + A = 168.

Simplifying further, we have: 3O + 5A = 168.

Now, we need to find integer solutions for O and A that satisfy this equation.

Finding Integer Solutions

To find integer solutions for O and A, we can use trial and error or a systematic approach.

Let's start by assuming O = 1 and finding the corresponding value of A: 3(1) + 5A = 168. 3 + 5A = 168. 5A = 165. A = 33.

However, A should be less than or equal to 168 since it represents the number of postcards collected by Anya. So, this solution is not valid.

Let's continue this process by assuming different values for O and finding the corresponding values of A.

After trying different values, we find that when O = 8 and A = 28, the equation is satisfied: 3(8) + 5(28) = 168.

Therefore, the valid solution is: - Natasha (N) collected 2O = 2(8) = 16 postcards. - Masha (M) collected 4A = 4(28) = 112 postcards. - Olya (O) collected 8 postcards. - Anya (A) collected 28 postcards.

Answer

Therefore, Natasha collected 16 postcards, Masha collected 112 postcards, Olya collected 8 postcards, and Anya collected 28 postcards.