Question

2 заводи за планом мали виготовити за місяць 360 верстатів. Перший завод виконав план на 112%, а другий - на 110%, тому обида виконали за місяць на 40 верстатів більше. Скільки верстатів понад планом виготовив кожен завод окремо

Answer 1

х (деталей) - план первого завода

360-х (деталей) - план второго завода

х*1,12+(360-х)*1,1=360+40

1,12х+396-1,1х=400

0,02х=4

х=4:0,02

х=200 (деталей) - должен был изготовить первый за вод по плану

360-200=160 (деталей) - должен был изготовить второй завод по плану

200*1,12=224 (детали) - изготовил первый завод

160*1,1=176 (деталей) - изготовил второй завод

224-200=24 (детали) 

176-160=16 (деталей)

Ответ: на 24 детали больше плана изготовил первый завод, на 16 деталей больше плана изготовил второй завод

Answer 2

Problem Analysis

We are given that two factories were supposed to produce a total of 360 machines in a month. The first factory exceeded the plan by 112%, and the second factory exceeded the plan by 110%. As a result, both factories produced 40 machines more than planned. We need to determine how many machines each factory produced above the plan.

Solution

Let's assume that the first factory produced x machines above the plan. Then, the second factory produced (40 - x) machines above the plan, as the total number of machines produced above the plan is 40.

According to the given information, the first factory exceeded the plan by 112%, which means it produced 112% of the planned machines. Mathematically, this can be represented as:

x = 112% of the planned machines

Similarly, the second factory exceeded the plan by 110%, which can be represented as:

(40 - x) = 110% of the planned machines

To solve this system of equations, we can convert the percentages to decimals. 112% is equivalent to 1.12, and 110% is equivalent to 1.10.

Now, we can solve the system of equations:

x = 1.12 * planned machines (40 - x) = 1.10 * planned machines

Simplifying the equations, we get:

x = 1.12 * planned machines 40 - x = 1.10 * planned machines

Let's solve these equations to find the values of x and the planned machines.

Calculation

To solve the equations, we can use algebraic manipulation. Let's start by isolating x in the second equation:

40 - x = 1.10 * planned machines -x = 1.10 * planned machines - 40 x = -1.10 * planned machines + 40

Now, we can substitute the value of x in the first equation:

x = 1.12 * planned machines -1.10 * planned machines + 40 = 1.12 * planned machines

Simplifying further:

40 = 1.12 * planned machines + 1.10 * planned machines 40 = 2.22 * planned machines

Dividing both sides by 2.22:

planned machines = 40 / 2.22 planned machines ≈ 18.02

Now, we can substitute the value of planned machines back into the equation for x:

x = 1.12 * 18.02 x ≈ 20.16

Therefore, the first factory produced approximately 20.16 machines above the plan, and the second factory produced approximately (40 - 20.16) = 19.84 machines above the plan.

Answer

The first factory produced approximately 20.16 machines above the plan, while the second factory produced approximately 19.84 machines above the plan.

Note: The calculations are approximations due to rounding.