Question

у першому ящику лежало втричі більше столових приборів ніж в другому після того як з другого ящика переклали 12 столових приборів в перший в другому стало в чотири рази меньше

Answer 1

Ответ:

Нехай в другому ящику було x столових приборів. Тоді в першому ящику було 3x столових приборів. Після перекладання 12 приборів з другого ящика в перший, у першому ящику стало 3x + 12 приборів, а в другому — (x-12) приборів. За умовою задачі, другий ящик після перекладання містить в чотири рази менше приборів, тобто:

(x - 12) = 0,25 × (3x + 12)

Розв'язуючи це рівняння, отримуємо:

4x - 48 = 3x + 12

x = 60

Відповідь: в другому ящику було 60 столових приборів, а в першому — 3x = 180 приборів.

Answer 2

В першому ящику лежало втричі більше столових приборів ніж в другому. Після того, як з другого ящика переклали 12 столових приборів в перший, в другому ящику стало в чотири рази менше столових приборів.

Step 1: Determine the initial number of utensils in each drawer

Let's assume the initial number of utensils in the first drawer is x and the initial number of utensils in the second drawer is y.

Step 2: Determine the number of utensils after transferring 12 from the second drawer to the first drawer

After transferring 12 utensils from the second drawer to the first drawer, the number of utensils in the first drawer becomes x + 12 and the number of utensils in the second drawer becomes y - 12.

Step 3: Set up the equation based on the given information

According to the given information, the number of utensils in the first drawer is three times more than the number of utensils in the second drawer. This can be expressed as:

x + 12 = 3(y - 12)

Step 4: Solve the equation

Let's solve the equation to find the values of x and y.

Expanding the equation: x + 12 = 3y - 36

Rearranging the equation: x - 3y = -48

Now, we need another equation to solve for x and y. According to the given information, after transferring 12 utensils from the second drawer to the first drawer, the number of utensils in the second drawer becomes four times less than the initial number. This can be expressed as:

y - 12 = (1/4)y

Step 5: Solve the second equation

Let's solve the second equation to find the value of y.

Expanding the equation: y - 12 = (1/4)y

Multiplying both sides by 4 to eliminate the fraction: 4y - 48 = y

Subtracting y from both sides: 3y = 48

Dividing both sides by 3: y = 16

Step 6: Substitute the value of y into the first equation to find x

Now that we have the value of y, let's substitute it into the first equation to find the value of x.

x - 3(16) = -48

Simplifying the equation: x - 48 = -48

Adding 48 to both sides: x = 0

Step 7: Verify the solution

To verify the solution, let's check if the given conditions are satisfied: - The initial number of utensils in the first drawer is 0. - The initial number of utensils in the second drawer is 16. - After transferring 12 utensils from the second drawer to the first drawer, the number of utensils in the first drawer becomes 12, and the number of utensils in the second drawer becomes 4. - The number of utensils in the first drawer is three times more than the number of utensils in the second drawer. - After transferring 12 utensils from the second drawer to the first drawer, the number of utensils in the second drawer becomes four times less than the initial number.

Based on the given conditions, the solution x = 0 and y = 16 satisfies all the conditions.

Therefore, initially, the first drawer had 0 utensils, and the second drawer had 16 utensils. After transferring 12 utensils from the second drawer to the first drawer, the first drawer had 12 utensils, and the second drawer had 4 utensils.