Question

1690. Для базы данных, состоящей из трёх, чисел среднее арифмети- ческое и медиана равны 32. Найдите эти числа, если наибольшее число больше наименьшего в 3 раза. помогите пж на завтра надо с решением ​

Answer 1

Пусть наименьшее число равно x, тогда наибольшее число равно 3x.

Тогда среднее арифметическое трех чисел:

(3x + x + y)/3 = 32, где y - среднее число.

Выразим y:

4x + y = 96

Также заметим, что медиана равна 32, что означает, что y также равно 32.

Тогда:

4x + 32 = 96

4x = 64

x = 16

Таким образом, наименьшее число равно 16, среднее число равно 32, а наибольшее число равно 3x = 48.

Ответ: 16, 32, 48.

Answer 2

Problem Analysis

We are given that the average and median of a database consisting of three numbers are both equal to 32. Additionally, the largest number is three times greater than the smallest number. We need to find these three numbers.

Solution

Let's assume the three numbers in the database are x, y, and z, where x is the smallest, y is the median, and z is the largest number.

1. We know that the average of the three numbers is 32. The average is calculated by summing all the numbers and dividing by the total count. In this case, the sum of the three numbers is 3 * 32 = 96. So, we have the equation:

x + y + z = 96 2. We also know that the median is 32. The median is the middle value when the numbers are arranged in ascending order. Since y is the median, we have:

y = 32 3. Finally, we are given that the largest number is three times greater than the smallest number. Mathematically, this can be expressed as:

z = 3x Now, we can solve these equations to find the values of x, y, and z.

Substituting equation into equation we get:

x + 32 + z = 96

Substituting equation into the above equation, we get:

x + 32 + 3x = 96

Simplifying the equation:

4x + 32 = 96

Subtracting 32 from both sides:

4x = 64

Dividing both sides by 4:

x = 16

Using equation we can find z:

z = 3x = 3 * 16 = 48

Finally, using equation we can find y:

y = 32

Therefore, the three numbers in the database are x = 16, y = 32, and z = 48.

Answer: The three numbers in the database are 16, 32, and 48.

Explanation

In this problem, we were given the average and median of a database consisting of three numbers. By setting up equations based on the given information, we were able to solve for the values of the three numbers. The smallest number is 16, the median is 32, and the largest number is 48.