Question

Настя и мама приготовили 110 пельменей, причем Настя работала 2 часа, а мама 3 часа. Сколько пельменей делала каждая за 1 час, если Настя за 3 часа сделала на 9 пельменей больше, чем мама за 2 часа? ПОЖАЛУЙСТА надо решить СИСТЕМОЙ УРАВНЕНИЙ​

Answer 1

Ответ: х=19, у=24

Пошаговое объяснение:

Answer 2

Пошаговое объяснение:

надеюсь почерк понятен...

Answer 3

Problem Analysis

We are given that Nastya and her mother prepared 110 dumplings together. Nastya worked for 2 hours, and her mother worked for 3 hours. We need to determine how many dumplings each of them made per hour. Additionally, we know that Nastya made 9 more dumplings than her mother in 3 hours, while her mother made dumplings for 2 hours.

Solution

Let's assume that Nastya made x dumplings per hour, and her mother made y dumplings per hour.

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

1. Nastya made 9 more dumplings than her mother in 3 hours: - Nastya: 3x - Mother: 2y - Equation: 3x = 2y + 9

2. Nastya and her mother made a total of 110 dumplings: - Nastya: 2x - Mother: 3y - Equation: 2x + 3y = 110

We now have a system of equations that we can solve to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the substitution method.

From equation 1, we can express x in terms of y: 3x = 2y + 9 x = (2y + 9) / 3

Substituting this value of x into equation 2: 2((2y + 9) / 3) + 3y = 110

Simplifying the equation: (4y + 18) / 3 + 3y = 110 4y + 18 + 9y = 330 13y = 312 y = 24

Substituting the value of y back into equation 1 to find x: 3x = 2(24) + 9 3x = 48 + 9 3x = 57 x = 19

Answer

Therefore, Nastya made 19 dumplings per hour, and her mother made 24 dumplings per hour.

Please let me know if you need any further assistance!