Question

В некотором трехзначном числе поменяли местами цифры десятков и единиц,а цифру сотен увеличили на 7.В результате исходное число увеличилось на 646.Сколько таких трёхзначных чисел?

Answer 1

Пусть число АВС.
(А+7)*100+С*10+В=646+А*100+В*10+С
(А+6)*100+С*9-9В=646
Очевидно, А=1 (0 но быть равным не может и больше 1 тоже)
(С-В)*9=-54
В-С=6
Возможно: В=6, С=0 или В=7 С=1 или В=8 С=2 или В=9 С=3
Числа 160, 171, 182 и 193. 806-160=817-171=828-182=839-193=646
Ответ: Д) 4

Answer 2

Problem Analysis

We are given a three-digit number in which the tens and units digits have been swapped, and the hundreds digit has been increased by 7. The resulting number is 646 greater than the original number. We need to determine how many three-digit numbers satisfy these conditions.

Solution

Let's denote the original number as ABC, where A represents the hundreds digit, B represents the tens digit, and C represents the units digit. According to the given conditions, the new number is BAC, and the difference between the new number and the original number is 646.

To solve this problem, we can set up the following equations:

1. The new number is formed by swapping the tens and units digits: - New number = 100 * B + 10 * A + C - Original number = 100 * A + 10 * B + C

2. The hundreds digit of the new number is 7 greater than the original number: - A + 7 = B

3. The difference between the new number and the original number is 646: - New number - Original number = 646

Let's solve these equations step by step.

Step 1: Express the new number and the original number in terms of A, B, and C

From equation 1, we have: - New number = 100 * B + 10 * A + C - Original number = 100 * A + 10 * B + C

Step 2: Express the hundreds digit of the new number in terms of A

From equation 2, we have: - A + 7 = B

Step 3: Express the difference between the new number and the original number in terms of A, B, and C

From equation 3, we have: - New number - Original number = 646

Substituting the expressions from step 1 into equation 3, we get: - (100 * B + 10 * A + C) - (100 * A + 10 * B + C) = 646

Simplifying the