Question

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

Answer 1

Составим систему уравнений 
3х = 5у + 4
у = х - 8
Решать будем методом подстановки
 
Решение:
3х = 5(х - 8) + 4
3х = 5х - 40 +4
3х - 5х = -36
-2х = -36
х = 18
у = 18 - 8 
у = 10
Ответ:у = 10, х =18

Answer 2

Problem Analysis

The problem states that a student has two numbers. The difference between the first and second numbers is 8. The first number, when tripled and reduced by 4, is 5 times smaller than the second number increased by 5 times. We need to find the two numbers the student has in mind.

Solution

Let's assume the first number is x and the second number is y. We can set up the following equations based on the given information:

1. The difference between the first and second numbers is 8: y - x = 8. 2. The first number, when tripled and reduced by 4, is 5 times smaller than the second number increased by 5 times: 3x - 4 = 5(y + 5).

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 the substitution method:

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

Substituting this value of y into equation 2, we get:

3x - 4 = 5((x + 8) + 5).

Simplifying the equation:

3x - 4 = 5x + 65.

Rearranging the equation:

3x - 5x = 65 + 4.

-2x = 69.

x = -34.5.

Substituting the value of x