Question

Маша, Олена и София вместе собрали шесть целых одиннадцать двадцатых кг клубники. Маша и Олена вместе собрали четыре целых одну четвертую кг, а Олена и София вместе собрали четыре целых три двадцатых кг. Сколько кг клубники собрала каждая из девочек?

Answer 1

София = все вместе - (Маша + Олена) 6ц 11/20 - 4ц 1/4 (т.е. 4ц 5/20) = 2ц 6/20 Маша = 6ц 11/20 - 4ц 3/20 = 2ц 8/20 Олена = все вместе - (Маша + София) = 6ц 11/20 - (2ц 8/20 + 2ц 6/20) = 6ц 11/20 - 4ц 14/20 = 1ц 17/20

Answer 2

Problem Analysis

We are given the information that Masha, Olena, and Sofia together collected a total of 6 and 11/20 kg of strawberries. Additionally, we know that Masha and Olena together collected 4 and 1/4 kg, and Olena and Sofia together collected 4 and 3/20 kg. We need to determine how much each girl collected.

Solution

Let's assign variables to represent the amount of strawberries collected by each girl. Let's say Masha collected x kg, Olena collected y kg, and Sofia collected z kg.

From the given information, we can set up the following equations:

1. Masha + Olena + Sofia = 6 and 11/20 kg 2. Masha + Olena = 4 and 1/4 kg 3. Olena + Sofia = 4 and 3/20 kg

We can solve this system of equations to find the values of x, y, and z.

Solving the Equations

To solve the system of equations, we can use substitution or elimination method. Let's use the elimination method.

From equation 2, we can express Masha in terms of Olena: Masha = 4 and 1/4 kg - Olena

Substituting this value of Masha in equation 1, we get: (4 and 1/4 kg - Olena) + Olena + Sofia = 6 and 11/20 kg

Simplifying the equation: 4 and 1/4 kg + Sofia = 6 and 11/20 kg

Subtracting 4 and 1/4 kg from both sides: Sofia = 6 and 11/20 kg - 4 and 1/4 kg

Simplifying the subtraction: Sofia = 2 and 3/20 kg

Now, we know the value of Sofia. Let's substitute this value in equation 3 to find the value of Olena.

Olena + 2 and 3/20 kg = 4 and 3/20 kg

Subtracting 2 and 3/20 kg from both sides: Olena = 4 and 3/20 kg - 2 and 3/20 kg

Simplifying the subtraction: Olena = 2 and 1/10 kg

Finally, we can substitute the values of Olena and Sofia in equation 2 to find the value of Masha.

Masha + 2 and 1/10 kg = 4 and 1/4 kg

Subtracting 2 and 1/10 kg from both sides: Masha = 4 and 1/4 kg - 2 and 1/10 kg

Simplifying the subtraction: Masha = 2 and 1/20 kg

Answer

Based on the given information, Masha collected 2 and 1/20 kg of strawberries, Olena collected 2 and 1/10 kg of strawberries, and Sofia collected 2 and 3/20 kg of strawberries.

Note: The answer has been calculated based on the given information and the solution process described above.