Question

Токарь за три дня изготовил 80 деталей. В первый день он выполнил 30 % всей работы. Известно, что количество деталей, изготовленных в первый день, составляет 60 % количества деталей , изготовленных во второй день. Сколько деталей изготовил токарь в третий день?

Answer 1

80/100= 0,8 деталей на 1 %
30*0,8 = 24 детали в первый день
24/60= 0,4 деталей на 1 % от числа деталей во второй день
0,4*100 = 40 деталей во второй день
80-(40+24) = 16 деталей в третий день
Ответ: 16

Answer 2

Problem Analysis

We are given that a lathe worker (tokar) manufactured 80 parts in three days. On the first day, he completed 30% of the total work. It is also known that the number of parts manufactured on the first day is 60% of the number of parts manufactured on the second day. We need to determine how many parts the lathe worker manufactured on the third day.

Solution

Let's break down the information given:

- Total number of parts manufactured in three days: 80 - Percentage of work completed on the first day: 30% - Number of parts manufactured on the first day is 60% of the number of parts manufactured on the second day.

To solve this problem, we can set up a system of equations.

Let's assume: - Number of parts manufactured on the first day = x - Number of parts manufactured on the second day = y - Number of parts manufactured on the third day = z

From the given information, we can set up the following equations:

Equation 1: x + y + z = 80 (since the total number of parts manufactured in three days is 80)

Equation 2: x = 0.3 * (x + y + z) (since the percentage of work completed on the first day is 30%)

Equation 3: x = 0.6 * y (since the number of parts manufactured on the first day is 60% of the number of parts manufactured on the second day)

We can solve this system of equations to find the values of x, y, and z.

Solving the System of Equations

Let's solve the system of equations using substitution:

From Equation 2, we have: x = 0.3 * (x + y + z) x = 0.3x + 0.3y + 0.3z

Subtracting 0.3x from both sides, we get: 0.7x = 0.3y + 0.3z

Dividing both sides by 0.7, we get: x = (0.3y + 0.3z) / 0.7

Since we know from Equation 3 that x = 0.6y, we can substitute this value into the equation above:

0.6y = (0.3y + 0.3z) / 0.7

Multiplying both sides by 0.7, we get: 0.42y = 0.3y + 0.3z

Subtracting 0.3y from both sides, we get: 0.12y = 0.3z

Dividing both sides by 0.12, we get: y = 2.5z

Now, we can substitute the value of y back into Equation 3:

x = 0.6y x = 0.6 * 2.5z x = 1.5z

We can substitute the values of x and y into Equation 1:

x + y + z = 80 1.5z + 2.5z + z = 80 5z = 80 z = 16

Therefore, the lathe worker manufactured 16 parts on the third day.

Answer

The lathe worker manufactured 16 parts on the third day.