Question

Сумма цифр двухзначного числа равна 7. Если его цифры переставить местами,то полученное число будет на 9 единиц меньше начального.Найдите начальное число. Помогите срочно

Answer 1

Начальное число: 43 (4+3=7)
меняем местами цифры: 34
43-34=9

Answer 2

Problem Analysis

We are given a two-digit number whose digits sum up to 7. If we reverse the digits of this number, the resulting number will be 9 less than the original number. We need to find the original number.

Solution

Let's assume the original number is represented as AB, where A is the tens digit and B is the units digit. According to the problem statement, we have the following equations:

1. A + B = 7 (Equation 1) 2. 10B + A = 10A + B - 9 (Equation 2)

To solve this system of equations, we can substitute Equation 1 into Equation 2 and simplify:

10B + A = 10A + B - 9 9B - 9A = -9 B - A = -1 (Equation 3)

Now we have two equations: Equation 1 and Equation 3. We can solve this system of equations to find the values of A and B.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution. From Equation 3, we have B - A = -1. Rearranging this equation, we get B = A - 1.

Substituting this value of B into Equation 1, we get:

A + (A - 1) = 7 2A - 1 = 7 2A = 8 A = 4

Now that we have the value of A, we can substitute it back into Equation 1 to find B:

4 + B = 7 B = 7 - 4 B = 3

Therefore, the original number is 43.

Answer

The original number is 43.

Verification

Let's verify our answer by checking if the sum of the digits of the original number is 7 and if the reversed number is 9 less than the original number.

The sum of the digits of 43 is 4 + 3 = 7, which matches the given condition.

The reversed number of 43 is 34. If we subtract 9 from 43, we get 34. Therefore, the reversed number is indeed 9 less than the original number.

Our answer is verified to be correct.