Question

а) В первой бригаде на 3 человека меньше, чем во второй , а во второй бригаде на 5 человек больше ,чем в третьей. Сколько человек в каждой бригаде ,если во всех трёх 52 человека ? б ) На второй полке книг на 5 больше , чем на первой, но на 5 меньше, чем на третьей . Всего на полках 105 книг . Сколько книг на каждой полке ?

Answer 1

а) х- во второй
 х-3 это в первой
 х-5 это в третьей
 х+(х-3)+(х-5)=52
 3*х=60
 х=20
 20-3=17
 20-5=15

 

б)На первой полке - 30, на второй - 35, на третьей - 40.
105-5-(5+5)=90
90:3=30 - первая .
30+5=35 - вторая .
35+5=40 - третья .

Answer 2

Task: Solving Equations

a) Let's solve the equation to find the number of people in each brigade.

Let's assume: - The number of people in the first brigade is represented by x. - The number of people in the second brigade is represented by y. - The number of people in the third brigade is represented by z.

According to the given information: - In the first brigade, there are 3 fewer people than in the second brigade: x = y - 3. - In the second brigade, there are 5 more people than in the third brigade: y = z + 5. - The total number of people in all three brigades is 52: x + y + z = 52.

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

Substituting the value of y from the second equation into the first equation, we get: x = (z + 5) - 3.

Substituting the values of x and y into the third equation, we get: (z + 5) - 3 + z + z = 52.

Simplifying the equation: 3z + 2 = 52.

Subtracting 2 from both sides: 3z = 50.

Dividing both sides by 3: z = 16.67.

Since the number of people must be a whole number, we can round z to the nearest whole number, which is 17.

Substituting the value of z into the second equation, we get: y = 17 + 5 = 22.

Substituting the values of y and z into the first equation, we get: x = 22 - 3 = 19.

Therefore, there are 19 people in the first brigade, 22 people in the second brigade, and 17 people in the third brigade.

b) Let's solve the equation to find the number of books on each shelf.

Let's assume: - The number of books on the first shelf is represented by x. - The number of books on the second shelf is represented by y. - The number of books on the third shelf is represented by z.

According to the given information: - On the second shelf, there are 5 more books than on the first shelf: y = x + 5. - On the second shelf, there are 5 fewer books than on the third shelf: y = z - 5. - The total number of books on all three shelves is 105: x + y + z = 105.

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

Substituting the value of y from the first equation into the second equation, we get: x + 5 = z - 5.

Substituting the values of x and y into the third equation, we get: x + (x + 5) + (x + 5 + 5) = 105.

Simplifying the equation: 3x + 15 = 105.

Subtracting 15 from both sides: 3x = 90.

Dividing both sides by 3: x = 30.

Substituting the value of x into the first equation, we get: y = 30 + 5 = 35.

Substituting the values of x and y into the second equation, we get: z = 35 + 5 = 40.

Therefore, there are 30 books on the first shelf, 35 books on the second shelf, and 40 books on the third shelf.