Question

Катя решила задач в 2 раза меньше чем Маша и в 3 раза меньше чем Нина. Сколько задач решила каждая девочка если вместе они решили 36 задач. Помогите пожалуста решение

Answer 1

Пусть катя решила х , тогда маша 2х , а нина 3х
составим и решим уравнение
х+2х+3х=36
6х=36
х=6 задач решила катя
маша решила 6*2=12 задач
нина 6*3=18 задач

Answer 2

Problem Analysis

We are given the following information: - Katya solved the problems in 2 times less than Masha. - Katya solved the problems in 3 times less than Nina. - Together, they solved 36 problems.

We need to find out how many problems each girl solved.

Solution

Let's assume that Masha solved x problems.

According to the given information, Katya solved the problems in 2 times less than Masha, so Katya solved (x - 2x) = -x problems.

Similarly, Nina solved the problems in 3 times less than Nina, so Nina solved (x - 3x) = -2x problems.

Together, they solved 36 problems, so we can write the equation:

x + (-x) + (-2x) = 36

Simplifying the equation:

-2x = 36

Dividing both sides by -2:

x = -18

Since the number of problems cannot be negative, we can conclude that our assumption was incorrect.

Let's assume that Masha solved y problems.

According to the given information, Katya solved the problems in 2 times less than Masha, so Katya solved (y - 2y) = -y problems.

Similarly, Nina solved the problems in 3 times less than Nina, so Nina solved (y - 3y) = -2y problems.

Together, they solved 36 problems, so we can write the equation:

y + (-y) + (-2y) = 36

Simplifying the equation:

-2y = 36

Dividing both sides by -2:

y = -18

Again, the number of problems cannot be negative, so our assumption was incorrect.

Let's assume that Nina solved z problems.

According to the given information, Katya solved the problems in 2 times less than Masha, so Katya solved (2z) problems.

Similarly, Katya solved the problems in 3 times less than Nina, so Katya solved (3z) problems.

Together, they solved 36 problems, so we can write the equation:

z + 2z + 3z = 36

Simplifying the equation:

6z = 36

Dividing both sides by 6:

z = 6

Therefore, Nina solved 6 problems.

Katya solved 2 times less than Nina, so Katya solved 2 * 6 = 12 problems.

Masha solved 3 times less than Nina, so Masha solved 3 * 6 = 18 problems.

To summarize: - Nina solved 6 problems. - Katya solved 12 problems. - Masha solved 18 problems.

Answer

Nina solved 6 problems, Katya solved 12 problems, and Masha solved 18 problems.