Question

Есть 19 гирек массами 1г, 2г, ..., 19г, из которых 9 железных, 9 бронзовых и одна золотая. Известно, что масса всех бронзовых гирек на 90г меньше, чем масса всех железных. найдите массу золотой гирьки.

Answer 1

Золото как известно тяжелое и гирька золотая одна, то не сложно догадаться что вес уже известен - 19 грамм

Answer 2

Problem Analysis

We are given 19 weights, ranging from 1g to 19g, with 9 of them being made of iron, 9 made of bronze, and one made of gold. We also know that the total mass of the bronze weights is 90g less than the total mass of the iron weights. We need to find the mass of the gold weight.

Solution

Let's denote the mass of the gold weight as x.

The total mass of the iron weights is the sum of the masses of the iron weights, which is given by the sum of the arithmetic series from 1g to 9g: Total mass of iron weights = 1g + 2g + 3g + ... + 9g = (9/2)(1g + 9g) = 45g.

Similarly, the total mass of the bronze weights is the sum of the masses of the bronze weights, which is given by the sum of the arithmetic series from 10g to 19g: Total mass of bronze weights = 10g + 11g + 12g + ... + 19g = (9/2)(10g + 19g) = 135g.

According to the given information, the total mass of the bronze weights is 90g less than the total mass of the iron weights: Total mass of bronze weights = Total mass of iron weights - 90g.

Substituting the values we have: 135g = 45g - 90g.

Simplifying the equation: 135g = -45g.

This equation is not possible, as the mass cannot be negative. Therefore, there is an error in the given information or the problem statement.

Unfortunately, we cannot determine the mass of the gold weight with the given information.

If you have any further questions, please let me know.