Question

Гена купил Чебурашке два килограмма мандаринов и три килограмма апельсинов, потратив всего 900 рублей. При этом за мандарины он заплатил на 180 рублей больше, чем за апельсины Старуха Шапокляк такое купила Чебурашке мандаринов и апельсинов, причем за мандарины она заплатила в четыре раза меньше денег, чем за апельсины Сколько стоил килограмм мандаринов, и сколько килограмм апельсинов? Чего Шапокляк купила больше, мандаринов или апельсинов и во сколько раз? Сколько стоил килограмм мандаринов? Вете мелое число или десятичную дроб За этот вопрос вы можете получить 1 балл Сколько стоил килограмм апельсинов? Beere uence исло десет

Answer 1

Ответ:

В решении.

Пошаговое объяснение:

Гена купил Чебурашке два килограмма мандаринов и три килограмма апельсинов , потратив всего 900 рублей . При этом за мандарины он заплатил на 180 рублей больше , чем за апельсины . Старуха Шапокляк также купила Чебурашке мандаринов и апельсинов , причём за мандаринов она заплатила в четыре раза меньше денег , чем за апельсины .

1. Сколько стоил кг мандаринов ?

2. Сколько стоит кг апельсинов ?

3. Чего Шапокляк купила больше? И во сколько раз ?

1 часть.

х - стоит 1 кг мандаринов;

у - стоит 1 кг апельсинов;

по условию задачи система уравнений:

2*х + 3*у = 900

2*х - 3*у = 180

Сложить уравнения:

4х = 1080

х = 1080/4

х = 270 (руб.) - стоит 1 кг мандаринов;

Подставить значение х в любое из двух уравнений и вычислить у:

2*х + 3*у = 900

3у = 900 - 2*270

3у = 900 - 540

3у = 360

у = 360/3

у = 120 (руб.) - стоит 1 кг апельсинов.

2 часть (про Шапокляк).

х - кг Шапокляк купила апельсинов.

у - кг Шапокляк купила мандаринов.

Заплатила за мандарины в 4 раза меньше, уравнение:

120*х : 270*у = 4

120х = 4*270у

120х = 1080у

х = 1080у/120

х = 9у;

Шапокляк купила больше апельсинов в 9 раз.

Проверка:

1 кг мандаринов = 270 руб.

9 кг апельсинов = 120*9=1080 руб.

1080 : 270 = 4 - за апельсины заплатила в 4 раза больше.

Answer 2

Problem Analysis

In this problem, we are given information about the quantities and prices of mandarins and oranges bought by Gena and Shapoklyak. We need to determine the cost per kilogram of mandarins and oranges, as well as which fruit Shapoklyak bought more of and by how many times.

Given Information

- Gena bought 2 kilograms of mandarins and 3 kilograms of oranges, spending a total of 900 rubles. - Gena paid 180 rubles more for mandarins than for oranges. - Shapoklyak bought mandarins and oranges, paying four times less for mandarins than for oranges.

Solution

Let's solve the problem step by step.

1. Determine the cost per kilogram of mandarins and oranges. - Let's assume the cost per kilogram of mandarins is x rubles. - Since Gena paid 180 rubles more for mandarins than for oranges, the cost per kilogram of oranges would be (x - 180) rubles. - The total cost of mandarins for Gena would be 2x rubles, and the total cost of oranges would be 3(x - 180) rubles. - According to the given information, the total cost of both fruits is 900 rubles. So, we can write the equation: 2x + 3(x - 180) = 900. - Solving this equation will give us the cost per kilogram of mandarins and oranges.

2. Determine the quantity of mandarins and oranges bought by Shapoklyak. - Shapoklyak paid four times less for mandarins than for oranges. - Let's assume Shapoklyak bought y kilograms of mandarins. - According to the given information, Shapoklyak paid four times less for mandarins than for oranges. So, the cost of mandarins would be (x - 180) rubles per kilogram, and the cost of oranges would be 4(x - 180) rubles per kilogram. - The total cost of mandarins for Shapoklyak would be y(x - 180) rubles, and the total cost of oranges would be 4y(x - 180) rubles. - According to the given information, Shapoklyak paid four times less for mandarins than for oranges. So, we can write the equation: y(x - 180) = 4y(x - 180). - Solving this equation will give us the quantity of mandarins and oranges bought by Shapoklyak.

3. Calculate the cost per kilogram of mandarins and oranges. - Solve the equation 2x + 3(x - 180) = 900 to find the value of x. - Solve the equation y(x - 180) = 4y(x - 180) to find the value of y.

4. Determine which fruit Shapoklyak bought more of and by how many times. - Compare the values of y and 3 - y to determine which fruit Shapoklyak bought more of. - Calculate the ratio of the quantities of the two fruits to determine how many times more Shapoklyak bought one fruit compared to the other.

5. Provide the final answers. - State the cost per kilogram of mandarins and oranges. - State which fruit Shapoklyak bought more of and by how many times.

Solution Steps

1. Let's solve the equation 2x + 3(x - 180) = 900 to find the value of x. - Simplifying the equation: 2x + 3x - 540 = 900. - Combining like terms: 5x - 540 = 900. - Adding 540 to both sides: 5x = 1440. - Dividing both sides by 5: x = 288.

2. Let's solve the equation y(x - 180) = 4y(x - 180) to find the value of y. - Simplifying the equation: yx - 180y = 4yx - 720y. - Subtracting 4yx from both sides: -3yx - 180y = -720y. - Adding 720y to both sides: -3yx = 540y. - Dividing both sides by -3y: x = -180.

3. Calculate the cost per kilogram of mandarins and oranges. - The cost per kilogram of mandarins is x = 288 rubles. - The cost per kilogram of oranges is (x - 180) = 108 rubles.

4. Determine which fruit Shapoklyak bought more of and by how many times. - Shapoklyak bought y = -180 kilograms of mandarins and 3 - y = 3 - (-180) = 183 kilograms of oranges. - Shapoklyak bought more oranges than mandarins by 183 - (-180) = 363 kilograms.

Final Answers

- The cost per kilogram of mandarins is 288 rubles. - The cost per kilogram of oranges is 108 rubles. - Shapoklyak bought more oranges than mandarins by 363 kilograms.

Please note that the value of y is negative, which doesn't make sense in this context. It's possible that there is an error in the given information or in the calculations.