Question

Алгебра 7 клас, дві бригади працювали на збиранні яблук.першого дня одна бригада працювала 5 год,а друга 4 год,при чому разом вони зібрали 40 ц яблук.Наступного дня бригади працювали з тією самою продуктивністю праці при цьому перша бригада зібрала за три год на 2ц більше ніж друга за2год.Скільки центнерів зібрала кожна бригада за1 год?

Answer 1

Нехай перша бригада за годину збирала $x$ яблук, а друга бригада $y$ яблук:

$5x+4y=40$

Друга умова запишеться у вигляді рівняння так:

$3x=2y+2$

Складемо обидва рівняння в систему та розв'яжемо її:

$\begin{cases}5x+4y=40 \\ 3x=2y+2 \end{cases}\\\begin{cases}5x+4y=40 \\ 3x-2y=2 \end{cases}\\\begin{cases}5x+4y=40 \\ 6x-4y=4 \end{cases}$

Складемо обидва рівняння:

$(5x+4y)+(6x-4y)=40+4\\11x=44\\x=44:11=4$

Ігрек знайдемо з першої умови:

$5 \cdot 4+4y=40\\4y=20\\y=5$

Відповідь: перша бригада 4 ц., друга — 5 ц.

Answer 2

Problem Analysis

We are given that two brigades worked together to collect apples for two days. On the first day, one brigade worked for 5 hours and the other brigade worked for 4 hours, and together they collected 40 centners of apples. On the second day, both brigades worked with the same productivity, and the first brigade collected 2 centners more than the second brigade in 3 hours, while the second brigade collected 2 centners in 2 hours. We need to find out how many centners of apples each brigade collected per hour.

Solution

Let's assume that the first brigade collected x centners of apples per hour, and the second brigade collected y centners of apples per hour.

From the given information, we can form the following equations:

1. On the first day, the total amount of apples collected by both brigades is 40 centners: - 5x + 4y = 40 [[1]]

2. On the second day, the first brigade collected 2 centners more than the second brigade in 3 hours, while the second brigade collected 2 centners in 2 hours: - 3x - 2y = 2 [[2]]

We can solve these equations to find the values of x and y.

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

Multiplying equation [[2]] by 2, we get: - 6x - 4y = 4 [[3]]

Adding equations [[1]] and [[3]], we eliminate the variable y: - 5x + 4y + 6x - 4y = 40 + 4 - 11x = 44 - x = 4

Substituting the value of x into equation [[1]], we can find the value of y: - 5(4) + 4y = 40 - 20 + 4y = 40 - 4y = 20 - y = 5

Therefore, the first brigade collected 4 centners of apples per hour, and the second brigade collected 5 centners of apples per hour.

Answer

Each brigade collected the following amount of apples per hour: - The first brigade collected 4 centners of apples per hour. - The second brigade collected 5 centners of apples per hour.