Question

вася задумал число, вычел из него 4, умножил на 5,прибавил 3, разделил на 7 и получил 9. какое число задумал вася?

Answer 1

Вася задумал число, вычел из него 4, умножил на 5, прибавил 3, разделил на 7 и получил 9. Какое число задумал Вася?

 

Пусть х - число которое задумал Вася, тогда

((х-4)·5+3):7=9

(5х-20+3):7=9

5х-17=9·7

5х-17=63

5х=63+17

5х=80

х=80:5

х=16

Ответ: Вася задумал число 16.

Проверка:

16-4·5+3:7=12·5+3:7=60+3:7=63:7=9

Answer 2

9*7=63

63-3=60

60:5=12

12+4=16

ответ: 16

Answer 3

Problem Analysis

Vasya has a number in mind. He subtracts 4 from it, multiplies the result by 5, adds 3, divides the sum by 7, and gets 9. We need to find the number Vasya had in mind.

Solution

Let's break down the problem step by step:

1. Vasya subtracts 4 from the number. 2. He multiplies the result by 5. 3. He adds 3 to the product. 4. He divides the sum by 7. 5. The result is 9.

To find the number Vasya had in mind, we need to reverse these steps.

Let's denote the unknown number as x.

1. Subtracting 4 from x: x - 4 2. Multiplying the result by 5: 5(x - 4) 3. Adding 3 to the product: 5(x - 4) + 3 4. Dividing the sum by 7: (5(x - 4) + 3) / 7 5. The result is 9: (5(x - 4) + 3) / 7 = 9

Now, we can solve this equation to find the value of x.

Solving the Equation

To solve the equation (5(x - 4) + 3) / 7 = 9, we can follow these steps:

1. Multiply both sides of the equation by 7 to eliminate the denominator: 7 * (5(x - 4) + 3) / 7 = 9 * 7 2. Simplify the equation: 5(x - 4) + 3 = 63 3. Distribute 5 to the terms inside the parentheses: 5x - 20 + 3 = 63 4. Combine like terms: 5x - 17 = 63 5. Add 17 to both sides of the equation: 5x - 17 + 17 = 63 + 17 6. Simplify the equation: 5x = 80 7. Divide both sides of the equation by 5 to solve for x: x = 80 / 5 8. Calculate the value of x: x = 16

Therefore, the number Vasya had in mind is 16.

Answer

The number Vasya had in mind is 16.

Verification

Let's verify our answer by substituting x = 16 into the original equation:

1. Subtracting 4 from 16: 16 - 4 = 12 2. Multiplying the result by 5: 5 * 12 = 60 3. Adding 3 to the product: 60 + 3 = 63 4. Dividing the sum by 7: 63 / 7 = 9

The result is indeed 9, which confirms that our answer is correct.