Question

Решите пожалуйста задачу с пояснениями. : Ребята получили на новогодней ёлке одинаковые подарки. Во всех подарках вместе было 123 апельсина и 82 яблока. Сколько ребят присутствовало на ёлке? Сколько апельсинов и сколько яблок было в каждом подарке?

Answer 1

Было 41 ребят.    Число 123 кратно 3, 123:3=41
123:41=3 апельсина было в каждом подарке
82:41=2 яблока  было в каждом подарке

Answer 2

Problem Analysis

We are given that a group of children received the same number of gifts at a New Year's tree. The total number of oranges in all the gifts is 123, and the total number of apples is 82. We need to determine the number of children present at the tree and the number of oranges and apples in each gift.

Solution

Let's assume there were x children present at the tree. Since each child received the same number of gifts, we can divide the total number of oranges and apples by x to find the number of oranges and apples in each gift.

Let's denote the number of oranges in each gift as o and the number of apples in each gift as a.

From the given information, we have the following equations:

1. Total number of oranges: o * x = 123 2. Total number of apples: a * x = 82

To solve these equations, we can divide the equation for the total number of oranges by the equation for the total number of apples:

(o * x) / (a * x) = 123 / 82

Simplifying the equation, we get:

o / a = 123 / 82

We can simplify the ratio of oranges to apples:

o / a = 3 / 2

Since the number of oranges and apples must be whole numbers, the ratio of 3:2 implies that there are 3 oranges for every 2 apples in each gift.

Now, we can substitute this ratio back into the equation for the total number of oranges:

3 * x = 123

Solving for x, we find:

x = 123 / 3 = 41

Therefore, there were 41 children present at the tree.

To find the number of oranges and apples in each gift, we can substitute the value of x into the equations for the total number of oranges and apples:

o * 41 = 123

a * 41 = 82

Solving these equations, we find:

o = 3

a = 2

Therefore, each gift contained 3 oranges and 2 apples.

Answer

There were 41 children present at the New Year's tree. Each gift contained 3 oranges and 2 apples.

Explanation

The problem states that the total number of oranges in all the gifts was 123 and the total number of apples was 82. By solving the equations and using the given information, we determined that there were 41 children present at the tree, and each gift contained 3 oranges and 2 apples.