Question

В январе два цеха изготовили 1080 деталей. в феврале первый цех увеличил выпуск деталей на 15% а второй на 12% в результате было изготовлено 1224 детали сколько деталей изготовил каждый цех в феврале

Answer 1

Х - изготовил в январе первый цех
у - изготовил в январе второй цех

Тогда в феврале первый цех изготовил:   х + 0,15х = 1,15х
                             второй цех изготовил:     у + 0,12у = 1,12у

{ x + y = 1080
{ 1,15x + 1,12y = 1224

{ y = 1080 - x
{ 1,15x + 1,12*(1080 - x) = 1224

1,15x + 1209,6 - 1,12x = 1224
0,03x = 1224 - 1209,6
0,03x = 14,4
       x = 14,4 : 0,03
       x = 480 (дет.) - изготовлено первым цехом в январе
       у = 1080-480 = 600 (дет.) - изготовлено вторым цехом в январе

В феврале изготовлено первым цехом:    
                                               1,15*480 = 552 (дет.)
                    изготовлено вторым цехом:
                                               1,12*600 = 672 (дет.)

Ответ: 552 детали - первый цех; 672 детали - второй цех.

Answer 2

Calculation of the Number of Parts Produced by Each Workshop in February

To calculate the number of parts produced by each workshop in February, we need to consider the initial production in January and the percentage increase in production for each workshop.

In January, two workshops produced a total of 1080 parts.

In February, the first workshop increased its production by 15%, and the second workshop increased its production by 12%. The total number of parts produced in February was 1224.

To find the number of parts produced by each workshop in February, we can set up the following equations:

Let x be the number of parts produced by the first workshop in February. Let y be the number of parts produced by the second workshop in February.

Equation 1: x + y = 1224 (total number of parts produced in February) Equation 2: x = 1080 + (15/100) * 1080 (increase in production for the first workshop) Equation 3: y = 1080 + (12/100) * 1080 (increase in production for the second workshop)

Now, let's solve these equations to find the values of x and y.

Solution:

From Equation 2: x = 1080 + (15/100) * 1080 x = 1080 + 0.15 * 1080 x = 1080 + 162 x = 1242

From Equation 3: y = 1080 + (12/100) * 1080 y = 1080 + 0.12 * 1080 y = 1080 + 129.6 y = 1209.6

Therefore, the first workshop produced 1242 parts in February, and the second workshop produced 1209.6 parts in February.

Please note that the number of parts produced by each workshop is rounded to the nearest whole number.