Question

Ученик задумал два числа.Разность первого и второго чисел равна 8.Утроенное первое число на 4 меньше, чем второе число,увеличенное в 5 раз.Какие числа задумал ученик?

Answer 1

Problem Analysis

The problem states that a student has two numbers, and the difference between the first and second numbers is 8. Additionally, the first number, when tripled and reduced by 4, is equal to the second number multiplied by 5. We need to find the two numbers.

Solution

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

From the given information, we can form two equations:

1. The difference between the first and second numbers is 8: x - y = 8. 2. The first number, when tripled and reduced by 4, is equal to the second number multiplied by 5: 3x - 4 = 5y.

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

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we can express x in terms of y: x = y + 8.

Substituting this value of x into equation 2, we get: 3(y + 8) - 4 = 5y.

Simplifying the equation: 3y + 24 - 4 = 5y, 3y + 20 = 5y, 20 = 5y - 3y, 20 = 2y.

Dividing both sides by 2, we find: y = 10.

Substituting this value of y back into equation 1, we can find x: x = 10 + 8, x = 18.

Therefore, the two numbers the student has in mind are 18 and 10.

Answer

The student has the numbers 18 and 10 in mind.