Question

В коробке лежат вилки и ложки, причем вилки составляют из них 70%. Затем из коробки убрали несколько ложек, после чего общее число столовых приборов в коробке стало равно 35, а доля вилок увеличилась до 80%. Сколько столовых приборов было в коробке изначально?

Answer 1

Problem Analysis

We are given a box containing forks and spoons, with forks making up 70% of the total number of utensils. Some spoons are then removed from the box, resulting in a total of 35 utensils in the box, with forks now making up 80% of the total. We need to determine the initial number of utensils in the box.

Solution

Let's assume the initial number of utensils in the box is x.

According to the given information, forks make up 70% of the total utensils. Therefore, the number of forks in the box initially is 0.7x.

After some spoons are removed, the total number of utensils in the box becomes 35. This can be represented as:

0.7x + (initial number of spoons) = 35

The proportion of forks in the box after the spoons are removed is 80%. Therefore, the number of forks in the box at this point is 0.8 times the total number of utensils:

0.8 * 35 = 0.7x

Now we can solve these two equations to find the initial number of utensils in the box.

Calculation

Let's solve the equations:

0.7x + (initial number of spoons) = 35 ---(1)

0.8 * 35 = 0.7x ---(2)

From equation (2), we can find the value of x:

0.8 * 35 = 0.7x

28 = 0.7x

x = 28 / 0.7

x = 40

Therefore, the initial number of utensils in the box was 40.

Answer

The initial number of utensils in the box was 40.