Question

Андрей задумал два числа . Утроенное первое число в 2 раза больше второго. Если же первое из задуманных чисел уменьшить на 11, оно станет в 2 раза меньше второго . Найдите задуманные числа.

Answer 1

Пусть x и y задуманные числа
3х = 2y
2(x - 11 ) = y
Решение
y = 1,5x
2x - 22 = 1,5x
0,5x = 22
x = 44 ( первое число )
1,5 • 44 = 66 ( второе число )
Ответ числа 44 и 66

Answer 2

Problem Analysis

Andrey has two numbers in mind. The first number, when tripled, is twice as large as the second number. However, if the first number is reduced by 11, it becomes half the size of the second number. We need to find the two numbers that Andrey has in mind.

Solution

Let's assume the first number is represented by x and the second number is represented by y.

According to the problem statement, we have two equations:

1. The tripled first number is twice as large as the second number: 3x = 2y.

2. If the first number is reduced by 11, it becomes half the size of the second number: (x - 11) = (1/2)y.

We can solve this system of equations to find the values of x and y.

Solving the Equations

Let's solve the system of equations using substitution or elimination method.

From equation 2, we can express x in terms of y: x = (1/2)y + 11.

Substituting this value of x into equation 1, we get: 3((1/2)y + 11) = 2y.

Simplifying the equation: (3/2)y + 33 = 2y.

Moving all terms to one side: 2y - (3/2)y = 33.

Combining like terms: (4/2)y - (3/2)y = 33.

Simplifying further: (1/2)y = 33.

Multiplying both sides by 2 to eliminate the fraction: y = 66.

Now, substituting this value of y back into equation 1, we can find the value of x: 3x = 2(66).

Simplifying the equation: 3x = 132.

Dividing both sides by 3: x = 44.

Therefore, the two numbers that Andrey has in mind are 44 and 66.

Answer

The two numbers that Andrey has in mind are 44 and 66.