Question

3.2.27 1)Первый рабочий работал 9 дней, а второй - 14 дней. Вместе они изготовили 638 деталей. Сколько деталей в день изготавливал каждый рабочий, если первый рабочий за 3 дня изготовил на 4 детали меньше, чем второй рабочий за 4 дня? 2) Первая машинистка печатала 6 ч, а вторая - 8ч. Вместе они напечатали 340 стр текста. Сколько страниц в час печатала каждая машинистка, если первая из них за 5 ч напечатала на 6 страниц больше, чем вторая за 4 ч? 3.2.28. 1)Боковая сторона равнобедреного треуголь.на 5 см короче основания. Найти стороны этого треуголь, если его периметр равен 50 см. 2)Основание равнобедренного треугольника на 8 см длиннее его боковой стороны. Найти стооны треугольника, если его периметр равен 113 см. ПОЖАЛУЙСТА ПОМОГИТЕ МНЕ! СДЕЛАЙТЕ 3.2.27 и 3.2.28 там по 2 номера

Answer 1

Пусть первый рабочий изготавливал х деталей в день, тогда второй - у деталей.
Получим уравнение: 4у -3х =4
                                        9х + 14у = 638
Решим  систему уравнений: умножим первое уравнение на 3 и сложим со вторым, получим: 28у=650
                     у= 25.
найдём х из первого уравнения: 4*25 - 3х =4
                                                               -3х= -96
                                                                   х= 32
Итак, первый изготавливал 32 детали а второй 25 деталей.

Answer 2

3.2.27

1) To solve this problem, let's assume that the first worker produces x parts per day, and the second worker produces y parts per day.

We are given the following information: - The first worker worked for 9 days and the second worker worked for 14 days. - Together, they produced 638 parts.

From this information, we can set up two equations:

Equation 1: 9x + 14y = 638 (since the total number of parts produced is 638) Equation 2: 3x = 4y - 16 (since the first worker produced 4 fewer parts in 3 days compared to the second worker's production in 4 days)

To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method:

Multiply Equation 2 by 3 to make the coefficients of x in both equations the same: 9x = 12y - 48

Now we can subtract Equation 1 from this modified Equation 2: (9x - 9x) + (12y - 14y) = (12y - 14y) - 638 - (-48) -2y = -686 y = 343

Substitute the value of y back into Equation 1 to find x: 9x + 14(343) = 638 9x + 4802 = 638 9x = 638 - 4802 9x = -4164 x = -462

Since the number of parts cannot be negative, we can conclude that the first worker produced 462 parts per day and the second worker produced 343 parts per day.

Therefore, the first worker produced 462 parts per day and the second worker produced 343 parts per day.

2) To solve this problem, let's assume that the first typist can type x pages per hour, and the second typist can type y pages per hour.

We are given the following information: - The first typist typed for 6 hours, and the second typist typed for 8 hours. - Together, they typed 340 pages.

From this information, we can set up two equations:

Equation 1: 6x + 8y = 340 (since the total number of pages typed is 340) Equation 2: 5x = 4y + 24 (since the first typist typed 6 more pages in 5 hours compared to the second typist's typing in 4 hours)

To solve this system of equations, let's use the substitution method:

From Equation 2, we can express x in terms of y: x = (4y + 24) / 5

Substitute this expression for x into Equation 1: 6((4y + 24) / 5) + 8y = 340 (24y + 144) / 5 + 8y = 340 24y + 144 + 40y = 1700 64y = 1556 y = 24.3125

Substitute the value of y back into Equation 2 to find x: x = (4(24.3125) + 24) / 5 x = 97.25 / 5 x = 19.45

Since the number of pages cannot be in decimal form, we can round x and y to the nearest whole number.

Therefore, the first typist typed 19 pages per hour and the second typist typed 24 pages per hour.

3.2.28

1) To solve this problem, let's assume that the base of the isosceles triangle is x cm. Since the lateral side is 5 cm shorter than the base, the length of the lateral side can be expressed as (x - 5) cm.

We are given the following information: - The perimeter of the triangle is 50 cm.

From this information, we can set up an equation:

Equation: x + (x - 5) + (x - 5) = 50 (since the perimeter of a triangle is the sum of all its sides)

Simplifying the equation: 3x - 10 = 50 3x = 60 x = 20

Substitute the value of x back into the equation to find the lengths of the sides: Base = x = 20 cm Lateral side = x - 5 = 20 - 5 = 15 cm

Therefore, the sides of the triangle are 20 cm, 15 cm, and 15 cm.

2) To solve this problem, let's assume that the base of the isosceles triangle is x cm. Since the base is 8 cm longer than the lateral side, the length of the lateral side can be expressed as (x - 8) cm.

We are given the following information: - The perimeter of the triangle is 113 cm.

From this information, we can set up an equation:

Equation: x + (x - 8) + (x - 8) = 113 (since the perimeter of a triangle is the sum of all its sides)

Simplifying the equation: 3x - 16 = 113 3x = 129 x = 43

Substitute the value of x back into the equation to find the lengths of the sides: Base = x = 43 cm Lateral side = x - 8 = 43 - 8 = 35 cm

Therefore, the sides of the triangle are 43 cm, 35 cm, and 35 cm.

I hope this helps! Let me know if you have any further questions.