Question

Упаковали несколько посылок,распределив между ними поровну 48 книг и 120 журналов.Сколько получилось посылок,если в каждой из них книг на 6 меньше,чем журналов

Answer 1

Пусть х - количество посылок,

48 : х - книг в одной посылке

120 : х - журналов в одной посылке

книг на 6 меньше, чем журналов, составим уравнение:

48 : х + 6 = 120 : х

48 : х - 120 : х = -6

( 48 - 120 ) : х = - 6

-72 : х = - 6

72 : х = 6

х = 72 : 6

х = 12 - посылок получилось

Ответ: 12 посылок.

Или же записать:

48/х + 6 = 120/х

48/х - 120х = -6

- 72х = -6

72х = 6

х = 72: 6

х = 12

Answer 2

Problem Analysis

We have several packages that contain a total of 48 books and 120 magazines. Each package has a different number of books and magazines, with the number of books being 6 less than the number of magazines. We need to determine how many packages were created.

Solution

Let's assume that the number of magazines in each package is x. According to the problem statement, the number of books in each package is 6 less than the number of magazines. Therefore, the number of books in each package is x - 6.

To find the number of packages, we need to divide the total number of books and magazines by the sum of the number of books and magazines in each package.

Let's calculate the number of packages:

1. The total number of books and magazines is 48 + 120 = 168. 2. The sum of the number of books and magazines in each package is (x + x - 6) = 2x - 6. 3. The number of packages is given by the equation: 168 / (2x - 6).

To solve this equation, we need to find the value of x that satisfies the equation.

Let's solve the equation to find the number of packages:

168 / (2x - 6) = y

where y represents the number of packages.

To solve for x, we can multiply both sides of the equation by (2x - 6):

168 = y(2x - 6)

Expanding the equation:

168 = 2xy - 6y

Rearranging the equation:

2xy - 6y - 168 = 0

Now we have a quadratic equation in terms of x. We can solve this equation to find the value of x.

Calculation

To solve the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 2y, b = -6y, and c = -168.

Substituting the values into the quadratic formula:

x = (-(-6y) ± √((-6y)^2 - 4 * 2y * (-168))) / (2 * 2y)

Simplifying the equation:

x = (6y ± √(36y^2 + 1344y)) / (4y)

Now we have two possible values for x. Let's calculate the number of packages for each value of x.

Calculation 1: x = (6y + √(36y^2 + 1344y)) / (4y)

Substituting the value of x into the equation for the number of packages:

y = 168 / (2 * ((6y + √(36y^2 + 1344y)) / (4y)) - 6)

Simplifying the equation:

y = 168 / (12y + 2√(36y^2 + 1344y) - 12)

Multiplying both sides of the equation by (12y + 2√(36y^2 + 1344y) - 12):

y(12y + 2√(36y^2 + 1344y) - 12) = 168

Expanding the equation:

12y^2 + 2y√(36y^2 + 1344y) - 12y - 2√(36y^2 + 1344y) = 168

Rearranging the equation:

12y^2 - 12y - 168 + 2y√(36y^2 + 1344y) - 2√(36y^2 + 1344y) = 0

Now we have a quadratic equation in terms of y. We can solve this equation to find the value of y.

Calculation 2: x = (6y - √(36y^2 + 1344y)) / (4y)

Substituting the value of x into the equation for the number of packages:

y = 168 / (2 * ((6y - √(36y^2 + 1344y)) / (4y)) - 6)

Simplifying the equation:

y = 168 / (12y - 2√(36y^2 + 1344y) - 12)

Multiplying both sides of the equation by (12y - 2√(36y^2 + 1344y) - 12):

y(12y - 2√(36y^2 + 1344y) - 12) = 168

Expanding the equation:

12y^2 - 2y√(36y^2 + 1344y) - 12y - 2√(36y^2 + 1344y) = 168

Rearranging the equation:

12y^2 - 12y - 168 - 2y√(36y^2 + 1344y) + 2√(36y^2 + 1344y) = 0

Now we have another quadratic equation in terms of y. We can solve this equation to find the value of y.

Conclusion

By solving the quadratic equations, we can find the values of y and then calculate the number of packages. However, the equations are quite complex and require further calculations. To simplify the process, we can use a numerical method or approximation to find the values of y and the number of packages.

Unfortunately, I am unable to perform the numerical calculations required to find the exact solution. However, you can use a calculator or a mathematical software program to solve the equations and find the number of packages.

Please let me know if there is anything else I can help you with.