Question

Из вазы взяли половину слив без пяти, затем взяли еще 2/3 оставшихся. После этого осталось 10 слив. Сколько слив было в начале?

Answer 1

1) 1-2/3=1/3 слив осталась
2) 10:1*3=30 слив осталось после того как забрали половину
3) 30-5=25 слив составляет половину
4) 25*2=50 слив было изначально

Answer 2

Problem Analysis

We are given the following information: - Half of the plums were taken out of the vase without five. - Then, two-thirds of the remaining plums were taken out. - After this, there were 10 plums left.

We need to determine the number of plums that were initially in the vase.

Solution

Let's assume that the initial number of plums in the vase is represented by the variable x.

According to the given information, the following steps were taken: 1. Half of the plums were taken out without five, which means x/2 - 5 plums were taken out. 2. Then, two-thirds of the remaining plums were taken out, which means (x - (x/2 - 5)) * (2/3) plums were taken out. 3. After this, there were 10 plums left, so we can set up the equation: x - (x/2 - 5) - (x - (x/2 - 5)) * (2/3) = 10.

Now, let's solve this equation to find the value of x.

Calculation

Simplifying the equation: x - (x/2 - 5) - (x - (x/2 - 5)) * (2/3) = 10

Expanding the equation: x - x/2 + 5 - (x - x/2 + 5) * (2/3) = 10

Simplifying further: x - x/2 + 5 - (x - x/2 + 5) * (2/3) = 10 x - x/2 + 5 - (2x/3 - x/3 + 10/3) = 10

Combining like terms: x - x/2 + 5 - (2x/3 - x/3 + 10/3) = 10 x - x/2 + 5 - 2x/3 + x/3 - 10/3 = 10

Combining like terms: x - x/2 - 2x/3 + x/3 + 5 - 10/3 = 10 x - 3x/6 - 4x/6 + 2x/6 + 15/3 - 10/3 = 10

Combining like terms: x - 3x/6 - 4x/6 + 2x/6 + 15/3 - 10/3 = 10 x - 5x/6 + 5/3 = 10

Combining like terms: x - 5x/6 + 5/3 = 10 6x/6 - 5x/6 + 5/3 = 10

Combining like terms: 6x/6 - 5x/6 + 5/3 = 10 (6x - 5x)/6 + 5/3 = 10

Simplifying: (6x - 5x)/6 + 5/3 = 10 x/6 + 5/3 = 10

Multiplying both sides by 6 to eliminate the fraction: 6 * (x/6 + 5/3) = 6 * 10 x + 10 = 60

Subtracting 10 from both sides: x + 10 - 10 = 60 - 10 x = 50

Answer

Therefore, there were 50 plums in the vase initially.