Question

Кладоискатели Артур, Боря, Витя и Гриша нашли 70 золотых монет. Каждый нашел хотя бы по одной монете. Артур нашел больше всех. Боря и Витя вместе нашли 45 монет. Сколько золотых монет нашел Гриша? ​

Answer 1

х+х+45=70

2х+45=70

2х=25

х=25/2

х=12,5

Answer 2

Problem Analysis

We have four treasure hunters named Arthur, Boris, Vitya, and Grisha who found a total of 70 gold coins. Each of them found at least one coin. Arthur found the most coins, and Boris and Vitya together found 45 coins. We need to determine how many gold coins Grisha found.

Solution

Let's break down the information given in the problem step by step to find the solution.

1. The total number of gold coins found by all the treasure hunters is 70. 2. Each treasure hunter found at least one coin. 3. Arthur found more coins than anyone else. 4. Boris and Vitya together found 45 coins.

Let's use this information to find the number of coins Grisha found.

Solution Steps

1. Let's assume the number of coins Arthur found as A. 2. Boris and Vitya together found 45 coins, so we can write the equation: B + V = 45, where B represents the number of coins Boris found and V represents the number of coins Vitya found. 3. Arthur found more coins than anyone else, so we can write the equation: A > B, A > V. 4. The total number of coins found by all the treasure hunters is 70, so we can write the equation: A + B + V + G = 70, where G represents the number of coins Grisha found. 5. Since each treasure hunter found at least one coin, we can assume that A ≥ 1, B ≥ 1, V ≥ 1, G ≥ 1.

Now, let's solve these equations to find the number of coins Grisha found.

Solution Calculation

From the equation B + V = 45, we can deduce that B = 45 - V.

Substituting this value of B in the equation A > B, we get A > 45 - V.

From the equation A + B + V + G = 70, we can substitute the value of B and rearrange the equation as follows: A + (45 - V) + V + G = 70.

Simplifying the equation, we get A + 45 + G = 70.

Substituting the value of A from the equation A > 45 - V, we get 45 - V + 45 + G = 70.

Simplifying further, we get 90 - V + G = 70.

Rearranging the equation, we get G - V = 70 - 90.

Simplifying, we get G - V = -20.

Since each treasure hunter found at least one coin, we can assume that G ≥ 1 and V ≥ 1.

Considering these constraints, the possible values for G and V are:

- G = 1, V = 2 - G = 2, V = 3 - G = 3, V = 4 - G = 4, V = 5 - G = 5, V = 6 - G = 6, V = 7 - G = 7, V = 8 - G = 8, V = 9 - G = 9, V = 10 - G = 10, V = 11 - G = 11, V = 12 - G = 12, V = 13 - G = 13, V = 14 - G = 14, V = 15 - G = 15, V = 16 - G = 16, V = 17 - G = 17, V = 18 - G = 18, V = 19 - G = 19, V = 20 - G = 20, V = 21

Since we are looking for the number of coins Grisha found, we can conclude that Grisha found 20 gold coins.

Answer

Grisha found 20 gold coins.

Please let me know if you need any further assistance.