Question

На прилавке лежат 10 гирек массой n,n+1,...,n+9. Продавец взял одну из них, после чего общий вес всех оставшихся составил 1543. Гирьку какого веса взял продавец? 100 БАЛЛОВ

Answer 1

Ответ:

154

Пошаговое объяснение:

Answer 2

Problem Analysis

In this problem, we are given that there are 10 weights on a counter with masses n, n+1, ..., n+9. The seller takes one of the weights, and the total weight of the remaining weights is 1543. We need to determine the weight of the weight that the seller took.

Solution

Let's assume that the seller took the weight with mass x. Since the total weight of the remaining weights is 1543, we can write the following equation:

(n + n+1 + ... + n+9) - x = 1543

To simplify the equation, we can use the formula for the sum of an arithmetic series:

10n + 45 - x = 1543

Simplifying further:

10n - x = 1498

Now, we need to find the value of x. To do this, we need to find the value of n. We can use the equation above to find n.

Let's solve the equation for n:

10n = 1498 + x

n = (1498 + x) / 10

Now, we can substitute the value of n back into the equation to find x:

10 * ((1498 + x) / 10) - x = 1498

Simplifying:

1498 + x - x = 1498

x = 1498

Therefore, the seller took the weight with a mass of 1498.

Answer

The weight that the seller took is 1498.