Question

четверо друзей отправились за грибами и набрали вместе 121 белый гриб. Первый из друзей набрал на 2 белых гриба больше, чем второй , а третий- на 3 меньше . чем четвертый. При этом четвертый из друзей набрал на 5 белых меньше, чем второй.Сколько белых грибов набрал первый из друзей?

Answer 1

Problem Analysis

Four friends went mushroom picking together and collected a total of 121 white mushrooms. The first friend picked 2 more white mushrooms than the second friend, while the third friend picked 3 fewer white mushrooms than the fourth friend. Additionally, the fourth friend picked 5 fewer white mushrooms than the second friend. We need to determine how many white mushrooms the first friend picked.

Solution

Let's assign variables to represent the number of white mushrooms picked by each friend: - Let x be the number of white mushrooms picked by the first friend. - Let y be the number of white mushrooms picked by the second friend. - Let z be the number of white mushrooms picked by the third friend. - Let w be the number of white mushrooms picked by the fourth friend.

We can set up a system of equations based on the given information: 1. The total number of white mushrooms collected is 121: x + y + z + w = 121. 2. The first friend picked 2 more white mushrooms than the second friend: x = y + 2. 3. The third friend picked 3 fewer white mushrooms than the fourth friend: z = w - 3. 4. The fourth friend picked 5 fewer white mushrooms than the second friend: w = y - 5.

We can solve this system of equations to find the values of x, y, z, and w.

Solving the System of Equations

Let's substitute the values from equations 2, 3, and 4 into equation 1 to eliminate variables and solve for y:

(y + 2) + y + (w - 3) + w = 121

Simplifying the equation:

2y + 2w - 1 = 121

2y + 2w = 122

Dividing both sides of the equation by 2:

y + w = 61

Now, let's substitute the value of w from equation 4 into the equation above:

y + (y - 5) = 61

Simplifying the equation:

2y - 5 = 61

2y = 66

Dividing both sides of the equation by 2:

y = 33

Now that we have the value of y, we can substitute it back into equation 4 to find the value of w:

w = y - 5 = 33 - 5 = 28

Finally, we can substitute the values of y and w into equation 2 to find the value of x:

x = y + 2 = 33 + 2 = 35

Therefore, the first friend picked 35 white mushrooms.

Answer

The first friend picked 35 white mushrooms.

Explanation

Based on the given information, we can solve the system of equations to find the number of white mushrooms picked by each friend. The first friend picked 2 more white mushrooms than the second friend, the third friend picked 3 fewer white mushrooms than the fourth friend, and the fourth friend picked 5 fewer white mushrooms than the second friend. By substituting the values of the variables into the equations, we find that the first friend picked 35 white mushrooms.