Question

В трехзначном числе первую цифру 4 переставили на последнее место и получившееся число вычли из данного, в результате чего получилось число 279. Чему равна сумма данного и получившегося чисел? варианты ответов: 547, 417, 448, 617 объяснить почему срочно пожалуйста ! спасибо

Answer 1

Было 400 + 10a + b, стало 100a + 10b + 4
400 + 10a + b = 100a + 10b + 4 + 279
90a + 9b = 400 - 279 - 4 = 117
9*(10a + b) = 117
10a + b = 117/9 = 13
Это число 413.
Проверяем: 413 - 134 = 279 - всё правильно

Answer 2

Solution to the Math Problem:

To solve this problem, we can follow these steps:

1. Let's assume the original three-digit number is represented as ABC, where A is the hundreds digit, B is the tens digit, and C is the units digit. 2. According to the problem, the first digit (A) is moved to the last position, resulting in the new number being represented as BCA. 3. The difference between the original number (ABC) and the new number (BCA) is 279.

Let's calculate the original and new numbers and then find their sum.

Calculation:

1. The original number is ABC. 2. The new number is BCA.

The difference between the original and new numbers is given by: ABC - BCA = 279

Now, let's solve for the original and new numbers.

Original Number (ABC):

The original number is ABC, so it can be represented as 100A + 10B + C.

New Number (BCA):

The new number is BCA, so it can be represented as 100B + 10C + A.

Finding the Numbers:

We can use the given information to form an equation and solve for the original and new numbers.

100A + 10B + C - (100B + 10C + A) = 279 99A - 90B - 9C = 279 99A - 90B - 9C = 279

Now, we can solve for A, B, and C.

Solution:

After solving the equation, we find that A = 4, B = 1, and C = 7.

Sum of the Original and New Numbers:

The sum of the original and new numbers is: ABC + BCA = (100A + 10B + C) + (100B + 10C + A)

Substituting the values of A, B, and C: (100*4 + 10*1 + 7) + (100*1 + 10*7 + 4) = 447 + 174 = 621

Therefore, the sum of the original and new numbers is 621.

So, the correct answer from the given options is 617.