Question

в цехе имелись токарные , фрезерные и шлифовальные станки. Токарные станки составляли 5/11 всех этих станков . Число шлифовальных станков составляло 2/5 числа токарных станков. Сколько всего станков этих видов было в цехе, если фрезерных было на 8 меньше, чем токарных?

Answer 1

1) 5/11*2/5=2/11 (всех станков) - составляли шлифовальные

2) 1-(5/11+2/11)=4/11 (всех станков) - составляли фрезерные станки

3) 5/11-4/11=1/11 (всех станков) - составляли 8 станков

4) 8*11=88 (ст.) - было всего

5) 88*5/11=40 (ст.) - токарных

6) 88*2/11=16 (ст.) - шлифовальных

7) 88*4/11=32 (ст.) - фрезерные

Ответ: всего в цеху было 88 станков, из них - 40 токарных, 16 шлифовальных и 32 фрезерных.

Answer 2

Problem Analysis

We are given the information that there are lathe, milling, and grinding machines in a workshop. The lathe machines make up 5/11 of all the machines, and the number of grinding machines is 2/5 of the number of lathe machines. We need to determine the total number of machines of these types in the workshop, given that there are 8 fewer milling machines than lathe machines.

Solution

Let's assume the number of lathe machines is represented by L, the number of milling machines by M, and the number of grinding machines by G.

From the given information, we can write the following equations: 1. The number of lathe machines is 5/11 of the total machines: L = (5/11)(L + M + G). 2. The number of grinding machines is 2/5 of the number of lathe machines: G = (2/5)L. 3. The number of milling machines is 8 fewer than the number of lathe machines: M = L - 8.

To solve this system of equations, we can substitute equation 2 into equation 1 and equation 3 into equation 1, and then solve for L.

Substituting equation 2 into equation 1: (2/5)L = (5/11)(L + M + (2/5)L).

Substituting equation 3 into equation 1: L = (5/11)(L + (L - 8) + (2/5)L).

Now we can solve these equations to find the value of L.

Calculation

Let's solve the equations step by step:

Substituting equation 2 into equation 1: (2/5)L = (5/11)(L + M + (2/5)L).

Simplifying: (2/5)L = (5/11)(L + L - 8 + (2/5)L).

Expanding: (2/5)L = (5/11)(8L/5 - 8 + (2/5)L).

Simplifying: (2/5)L = (5/11)(8L/5 - 8 + 2L/5).

Multiplying both sides by 55 to eliminate the denominators: 22L = 25(8L/5 - 8 + 2L/5).

Expanding: 22L = 25(8L/5) - 25(8) + 25(2L/5).

Simplifying: 22L = 32L - 200 + 10L.

Combining like terms: 22L = 42L - 200.

Moving the variables to one side and the constants to the other side: 42L - 22L = 200.

Simplifying: 20L = 200.

Dividing both sides by 20: L = 10.

Now that we have found the value of L, we can substitute it back into equation 3 to find the value of M: M = L - 8 = 10 - 8 = 2.

Finally, we can substitute the values of L and M into equation 2 to find the value of G: G = (2/5)L = (2/5)(10) = 4.

Therefore, the total number of machines of these types in the workshop is: - Lathe machines: 10 - Milling machines: 2 - Grinding machines: 4

Answer

There are a total of 10 lathe machines, 2 milling machines, and 4 grinding machines in the workshop.