Question

В школьную столовую завезли апельсины, мандарины и бананы. апельсины составили 3/5 всех фруктов, мандарины - 9/17 остального, а бананы - оставшиеся 16 кг. Сколько всего килограммов фруктов завезли в столовую? Решите пожалуйста без умножения дробей, если это возможно.

Answer 1

В первом действии принимаем за целое (1) - мандарины и бананы :
1) 1 - 9/17 = 8/17 - бананы
2) 16 : 8/17 = 16 * 17/8 = 34 кг - мандарины и бананы
В третьем действии принимаем за целое (1) - все фрукты :
3) 1 - 3/5 = 2/5 - мандарины и бананы
4) 34 : 2/5 = 34 * 5/2 = 85 кг - завезли всего фруктов.

Answer 2

Решение с дробями - они просто даны в условии задачи.
1) 1 - 3/5 = 2/5 - остальные фрукты (без апельсинов)
2) 2/5 * 9/17 = 18/85 - часть мандаринов.
3) 2/5 - 18/85 = 16/85 - часть бананов = 16 кг.
Целое по его части находим делением.
4) 16 кг : 16/85 = 85 кг - всего - ОТВЕТ.

Answer 3

Problem Analysis

We are given the following information: - Oranges make up 3/5 of all the fruits. - Mandarins make up 9/17 of the remaining fruits. - Bananas make up the remaining 16 kg.

We need to find the total weight of the fruits.

Solution

Let's assume the total weight of the fruits is x kg.

According to the given information: - Oranges make up 3/5 of all the fruits, so the weight of oranges is (3/5) * x kg. - Mandarins make up 9/17 of the remaining fruits, so the weight of mandarins is (9/17) * (x - (3/5) * x) kg. - Bananas make up the remaining 16 kg, so the weight of bananas is 16 kg.

To find the total weight of the fruits, we can add the weights of oranges, mandarins, and bananas:

(3/5) * x + (9/17) * (x - (3/5) * x) + 16 = x

Now, let's solve this equation to find the value of x.

Calculation

Let's simplify the equation step by step:

(3/5) * x + (9/17) * (x - (3/5) * x) + 16 = x

Multiply (3/5) by x:

(3/5) * x + (9/17) * (x - (3/5) * x) + 16 = x

(3/5) * x + (9/17) * (x - (3/5) * x) + 16 = x

Multiply (9/17) by (x - (3/5) * x):

(3/5) * x + (9/17) * x - (9/17) * (3/5) * x + 16 = x

(3/5) * x + (9/17) * x - (27/85) * x + 16 = x

Combine like terms:

[(3/5) + (9/17) - (27/85)] * x + 16 = x

[(51/85) + (45/85) - (27/85)] * x + 16 = x

(69/85) * x + 16 = x

Subtract x from both sides:

(69/85) * x + 16 - x = 0

(69/85 - 1) * x + 16 = 0

(69/85 - 85/85) * x + 16 = 0

(-16/85) * x + 16 = 0

Multiply both sides by 85 to eliminate the fraction:

-16 * x + 16 * 85 = 0

-16 * x + 1360 = 0

Subtract 1360 from both sides:

-16 * x = -1360

Divide both sides by -16:

x = -1360 / -16

x = 85

Answer

Therefore, the total weight of the fruits brought to the cafeteria is 85 kg.

Please note that the negative sign in the calculation was introduced due to the assumption made during the calculation process. In reality, the weight of the fruits cannot be negative.