Question

Ученик задумал 2 числа . Разность первого и второго чисел равно 7 . Произведение первого числа на 5 на 1 больше чем произведение второго числа на 3 . Какие числа задумал ученик

Answer 1

Х-первое
У-второе
Х-У=7 Х=7+У
5Х=3У+1 - решаем, подставляя вместо Х 7+У
5(7+У)=3У+1
35+5У=3У+1
5У-3У=1-35
2У=-34
У=-17
Х=7-17=-10
первое -10
второе -17

Answer 2

Problem Analysis

The problem states that a student has two numbers, and the difference between the first and second numbers is 7. Additionally, the product of the first number multiplied by 5 is 1 more than the product of the second number multiplied by 3. 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. According to the problem, we have the following equations:

1. x - y = 7 (Equation 1) 2. 5x = 3y + 1 (Equation 2)

To solve this 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 + 7 (Equation 3)

Substituting Equation 3 into Equation 2, we get: 5(y + 7) = 3y + 1

Simplifying the equation: 5y + 35 = 3y + 1

Bringing like terms to one side: 5y - 3y = 1 - 35 2y = -34

Dividing both sides by 2: y = -17

Substituting the value of y back into Equation 3, we can find the value of x: x = -17 + 7 x = -10

Therefore, the two numbers the student has in mind are -10 and -17.

Answer

The student has the numbers -10 and -17 in mind.