Question

сумма цифр двухзначного числа равна 15.Если поменять его цифры местами, то получим число,которое меньше данного на 9. Найдите данное число. ПОМОГИТЕ С ОБЪЯСНЕНИЕМ ПЛИИИИЗ. я видела ответы, но там везде был вставлена 10, хотя ее не было в задаче. помогите 50 БАЛЛОВ с объяснением

Answer 1

Пошаговое объяснение:

Дане число буде 87.

Сума його чисел 15 (8+7=15)

Якщо поміняти місцями, то виходить число 78, яке на 9 буде менше ніж дане число.

Answer 2

Problem Analysis

To solve this problem, we need to find a two-digit number whose digits sum up to 15. When we swap the digits, the resulting number is 9 less than the original number. Let's break down the problem step by step.

Step 1: Finding the original number

Let's assume the original number is represented as AB, where A is the tens digit and B is the ones digit. According to the problem, the sum of the digits is 15. So we have the equation:

A + B = 15

Step 2: Finding the number after swapping the digits

When we swap the digits, the resulting number is BA. According to the problem, this number is 9 less than the original number. So we have the equation:

10B + A = 10A + B - 9

Simplifying this equation, we get:

9B - 9A = -9

Step 3: Solving the system of equations

We now have a system of two equations:

A + B = 15 9B - 9A = -9

We can solve this system of equations to find the values of A and B.

Solution

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

From the first equation, we can express A in terms of B:

A = 15 - B

Substituting this value of A into the second equation, we get:

9B - 9(15 - B) = -9

Simplifying this equation, we get:

9B - 135 + 9B = -9 18B - 135 = -9 18B = 126 B = 7

Substituting the value of B back into the first equation, we get:

A + 7 = 15 A = 8

Therefore, the original number is 87.

Conclusion

The two-digit number that satisfies the given conditions is 87.

Answer 3

To find the two-digit number described in the problem, let's break down the information given step by step:

1. The sum of the digits of the two-digit number is 15. 2. If we swap the digits of the number, we get a number that is 9 less than the original number.

Let's solve this problem together:

Step 1: Finding the possible values for the tens digit

Since the sum of the digits is 15, the tens digit and the units digit must add up to 15. Let's consider the possible values for the tens digit:

- If the tens digit is 1, the units digit would be 15 - 1 = 14, which is not a valid digit for a two-digit number. - If the tens digit is 2, the units digit would be 15 - 2 = 13, which is also not a valid digit for a two-digit number. - If the tens digit is 3, the units digit would be 15 - 3 = 12, which is a valid digit for a two-digit number.

Step 2: Finding the possible values for the units digit

Now that we have the possible values for the tens digit, let's find the corresponding units digit for each case:

- If the tens digit is 3, the units digit would be 12.

Step 3: Forming the two-digit number

Based on the above analysis, the two-digit number that satisfies the given conditions is 32.

Explanation:

When we swap the digits of 32, we get 23. According to the problem, this number should be 9 less than the original number. Let's verify this:

- 32 - 9 = 23

Therefore, the two-digit number that satisfies the given conditions is indeed 32.

I hope this explanation helps! Let me know if you have any further questions.