Question

Две мастерские должны были пошить по 96 курток.Первая мастерская шила в день на 4 куртки больше,поэтому закончила работы на два дня раньше.Сколько курток в день шила каждая мастерская?Решите с помощью уравнения.

Answer 1

Х. х+4 куртки в день
96÷х=а. а×х=96. а=96/х
96÷(х+4)=а-2 (х+4)(а-2)=96
(х+4)(96/х-2)=96
96-2х+384/х-8-96=0
-2х+384/х-8=0 умножем на х
-2х^2-8х+384=0
D=64+3072=3136=56^2
х1=8+56/4=64/-4= -16так как нам не нужен отрицательный корень сы берем только х2
х1=8-56/4= -48/-4= 12 курток
х+4=12+4=16 курток
ответ: 12 и 16 курток шили в день

Answer 2

Problem Analysis

We are given that two workshops were tasked with sewing a total of 96 jackets. The first workshop sewed 4 jackets more per day and finished the work two days earlier than the second workshop. We need to determine how many jackets each workshop sewed per day.

Solution

Let's assume that the second workshop sewed x jackets per day. Since the first workshop sewed 4 jackets more per day, they sewed x + 4 jackets per day.

We can set up the following equation based on the given information:

(x + 4) * (number of days for the first workshop) = x * (number of days for the second workshop)

We know that the total number of jackets is 96, so we can also set up the equation:

(x + 4) * (number of days for the first workshop) + x * (number of days for the second workshop) = 96

Let's solve these equations to find the values of x and the number of days for each workshop.

Solution Steps

1. Let's assume the number of days for the second workshop is d days. 2. The number of days for the first workshop will be d - 2 (since they finished two days earlier). 3. Substitute these values into the equations and solve for x.

Detailed Solution

Let's solve the equations to find the number of jackets each workshop sewed per day.

Equation 1: (x + 4) * (number of days for the first workshop) = x * (number of days for the second workshop)

Equation 2: (x + 4) * (number of days for the first workshop) + x * (number of days for the second workshop) = 96

Let's substitute the values:

Equation 1: (x + 4) * (d - 2) = x * d

Equation 2: (x + 4) * (d - 2) + x * d = 96

Expanding Equation 1:

xd + 4d - 2x - 8 = xd

4d - 2x - 8 = 0

Expanding Equation 2:

xd + 4d - 2x - 8 + xd = 96

2xd + 4d - 2x - 8 = 96

2xd - 2x + 4d = 104

2(xd - x) + 4d = 104

2x(d - 1) + 4d = 104

2x(d - 1) = 104 - 4d

x(d - 1) = 52 - 2d

x = (52 - 2d) / (d - 1)

Now, let's substitute the value of x in Equation 2 and solve for d:

((52 - 2d) / (d - 1) + 4) * (d - 2) + (52 - 2d) * d = 96

Simplifying the equation:

((52 - 2d) + 4(d - 1)) * (d - 2) + (52 - 2d) * d = 96

(52 - 2d + 4d - 4) * (d - 2) + (52 - 2d) * d = 96

(2d + 48) * (d - 2) + (52 - 2d) * d = 96

Expanding the equation:

2d^2 - 4d + 48d - 96 + 52d - 2d^2 = 96

48d - 96 + 52d = 96

100d - 96 = 96

100d = 192

d = 1.92

Since the number of days cannot be a decimal, we can round it to the nearest whole number. Therefore, the number of days for the second workshop is 2.

Now, let's substitute the value of d in Equation 1 to find x:

x = (52 - 2 * 2) / (2 - 1)

x = 48 / 1

x = 48

Therefore, the second workshop sewed 48 jackets per day and the first workshop sewed 48 + 4 = 52 jackets per day.

Answer

The second workshop sewed 48 jackets per day, while the first workshop sewed 52 jackets per day.