Question

Бригада из столяров, моляров и жестянщиков, всего 12 рабочих, несет 12 бревен. Каждый столяр несет по два бревна. Каждый маляр несет по половине бревна, каждый жестянщик несет по четверти бревна. Сколько в бригаде столяров, сколько маляров и сколько жестянщиков, если известно, что столяров больше одного, но меньше, чем маляров, а маляров меньше, чем жестянщиков?

Answer 1

12-10x=76x-21x
14+15=29
29+17x=27 маляров

Answer 2

Problem Analysis

We are given a brigade consisting of carpenters, painters, and tinworkers, with a total of 12 workers. Each worker carries a certain number of logs. Carpenters carry 2 logs each, painters carry half a log each, and tinworkers carry a quarter of a log each. We need to determine the number of carpenters, painters, and tinworkers in the brigade, given that there is more than one carpenter, fewer painters than tinworkers, and the number of carpenters is less than the number of painters.

Solution

Let's assume the number of carpenters in the brigade is C, the number of painters is P, and the number of tinworkers is T.

From the given information, we can form the following equations:

1. The total number of workers in the brigade is 12: - C + P + T = 12

2. Each carpenter carries 2 logs: - Total logs carried by carpenters = 2C

3. Each painter carries half a log: - Total logs carried by painters = 0.5P

4. Each tinworker carries a quarter of a log: - Total logs carried by tinworkers = 0.25T

5. The total number of logs carried by the brigade is 12: - Total logs carried = 2C + 0.5P + 0.25T = 12

We can now solve these equations to find the values of C, P, and T.

Solving the Equations

Let's substitute equation 1 into equation 5 to eliminate one variable:

2C + 0.5P + 0.25T = 12 2C + 0.5P + 0.25(12 - C - P) = 12 2C + 0.5P + 3 - 0.25C - 0.25P = 12 1.75C + 0.25P = 9

Now, let's simplify equation 1:

C + P + T = 12 C + P = 12 - T

Substituting this into equation 1.75C + 0.25P = 9:

1.75C + 0.25(12 - T) = 9 1.75C + 3 - 0.25T = 9 1.75C - 0.25T = 6

We now have a system of two equations with two variables:

1.75C + 0.25P = 9 1.75C - 0.25T = 6

We can solve this system of equations to find the values of C, P, and T.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution. Let's solve equation 1.75C + 0.25P = 9 for P:

0.25P = 9 - 1.75C P = (9 - 1.75C) / 0.25 P = 36 - 7C

Now, let's substitute this value of P into equation 1.75C - 0.25T = 6:

1.75C - 0.25T = 6 1.75C - 0.25(36 - 7C) = 6 1.75C - 9 + 1.75C = 6 3.5C = 15 C = 15 / 3.5 C ≈ 4.29

Since the number of carpenters cannot be a fraction, we can round C to the nearest whole number:

C ≈ 4

Now, let's substitute this value of C into P = 36 - 7C:

P = 36 - 7(4) P = 36 - 28 P = 8

Finally, let's substitute the values of C and P into the equation C + P + T = 12 to find T:

4 + 8 + T = 12 T = 12 - 4 - 8 T = 0

Answer

Based on the given information, the brigade consists of approximately 4 carpenters, 8 painters, and 0 tinworkers.

Please note that the number of carpenters, painters, and tinworkers may not be whole numbers due to rounding in the calculations.