Question

В конторе скучают программисты. Известно, что половина программистов и еще 2 играют в игры на рабочем компьютере, половина всех оставшихся и еще 3 пьют сок в столовой, а треть нового остатка и последние 4 программиста греют мясо в микроволновке. Сколько всего программистов в конторе?

Answer 1

Ответ:

Всего было 40 программистов.

Пошаговое объяснение:

Сколько всего программистов в конторе?

Пусть в конторе х программистов, тогда играют в игры :

$\displaystyle \frac{1}{2} x +2$ программистов .

Остаток : $\displaystyle x - \frac{1}{2}x-2=\frac{1}{2}x-2$

Пьют сок :

$\displaystyle \frac{1}{2}*(\frac{1}{2}x -2)+3=\frac{1}{4}x-1+3=\frac{1}{4}x+2$ программист

Новый остаток :

$\displaystyle \frac{1}{2}x-2 -\frac{1}{4}x-2=\frac{1}{4}x-4$

Греют мясо :

$\displaystyle \frac{1}{3}*(\frac{1}{4}x-4)+4=\frac{1}{12}x-\frac{4}{3} +4=\frac{1}{12}x+\frac{8}{3}$

Получаем уравнение :

$\displaystyle x=\frac{1}{2}x+2+\frac{1}{4}x+2+\frac{1}{12}x+\frac{8}{3}\\ \\ x=\frac{10}{12}x+\frac{20}{3} \\ \\ x-\frac{10}{12}x=\frac{20}{3}\\ \\ \frac{2x}{12} =\frac{20}{3}$

по правилу пропорции :

6х = 12 * 20

6х = 240

х = 240 : 6

х = 40 программистов

Всего было 40 программистов.

Answer 2

Problem Analysis

We are given the following information about the programmers in a company: - Half of the programmers play games on their work computers, and an additional 2 programmers play games. - Half of the remaining programmers drink juice in the cafeteria, and an additional 3 programmers drink juice. - A third of the remaining programmers warm up meat in the microwave, and the last 4 programmers warm up meat.

We need to determine the total number of programmers in the company.

Solution

Let's solve this problem step by step.

Step 1: Let's assume the total number of programmers in the company is P.

Step 2: Half of the programmers play games on their work computers, so the number of programmers playing games is P/2. Additionally, 2 more programmers play games, so the total number of programmers playing games is P/2 + 2.

Step 3: Half of the remaining programmers drink juice in the cafeteria, so the number of programmers drinking juice is (P - (P/2 + 2))/2. Additionally, 3 more programmers drink juice, so the total number of programmers drinking juice is (P - (P/2 + 2))/2 + 3.

Step 4: A third of the remaining programmers warm up meat in the microwave, so the number of programmers warming up meat is (P - (P/2 + 2) - ((P - (P/2 + 2))/2 + 3))/3. Additionally, the last 4 programmers warm up meat, so the total number of programmers warming up meat is (P - (P/2 + 2) - ((P - (P/2 + 2))/2 + 3))/3 + 4.

Step 5: The sum of the programmers playing games, drinking juice, and warming up meat should be equal to the total number of programmers in the company. Therefore, we can set up the following equation:

(P/2 + 2) + ((P - (P/2 + 2))/2 + 3) + ((P - (P/2 + 2) - ((P - (P/2 + 2))/2 + 3))/3 + 4) = P

Now, let's solve this equation to find the value of P.

Calculation

(P/2 + 2) + ((P - (P/2 + 2))/2 + 3) + ((P - (P/2 + 2) - ((P - (P/2 + 2))/2 + 3))/3 + 4) = P

Simplifying the equation:

(P/2 + 2) + ((P - P/2 - 2)/2 + 3) + ((P - P/2 - 2 - (P - P/2 - 2)/2 - 3)/3 + 4) = P

(P/2 + 2) + ((P/2 - 2)/2 + 3) + ((P/2 - 2 - (P/2 - 2)/2 - 3)/3 + 4) = P

(P/2 + 2) + (P/4 - 1 + 3) + (P/6 - 1 - (P/4 - 1)/2 - 3)/3 + 4) = P

Multiplying through by 12 to eliminate fractions:

6(P/2 + 2) + 3(P/4 - 1 + 3) + 4(P/6 - 1 - (P/4 - 1)/2 - 3)/3 + 4) = 12P

6P + 24 + 3P/4 - 3 + 9 + 4P/6 - 4 - (P/4 - 1)/2 - 3)/3 + 4) = 12P

6P + 24 + 3P/4 - 3 + 9 + 4P/6 - 4 - (P/4 - 1)/2 - 3)/3 + 4) = 12P

24 + 9 - 3 - 4 - 3 + 4 = 12P - 6P - 3P/4 - 4P/6 + (P/4 - 1)/2

27 = 3P/4 - 4P/6 + (P/4 - 1)/2

27 = 3P/4 - 2P/3 + P/8 - 1/2

27 = (6P - 8P + 3P - 4)/24 - 1/2

27 = (P - 4)/24 - 1/2

Multiplying through by 24 to eliminate fractions:

648 = P - 4 - 12

648 = P - 16

P = 648 + 16

P = 664

Answer

There are a total of 664 programmers in the company.