Question

В мастерской сшили одинаковые костюмы для мальчиков и одинаковые - для девочек. На костюмы для мальчиков потратили 54 м ткани, а для девочек - 48 м. Костюмов для мальчиков сшили на 2 больше, чем для девочек, причем расход ткани на любой один костюм была одинаковой. Сколько сшили костюмов для мальчиков? для девочек

Answer 1

Problem Analysis

We are given that a workshop has sewn identical costumes for boys and identical costumes for girls. The workshop used 54 meters of fabric for the boys' costumes and 48 meters of fabric for the girls' costumes. The number of boys' costumes is 2 more than the number of girls' costumes, and the fabric used for each costume is the same. We need to determine how many costumes were sewn for boys and how many were sewn for girls.

Solution

Let's assume that the number of costumes sewn for girls is x. Since the number of boys' costumes is 2 more than the number of girls' costumes, the number of boys' costumes can be expressed as x + 2.

We are also given that the fabric used for each costume is the same. Therefore, we can set up the following equation based on the fabric used for boys' and girls' costumes:

Fabric used for boys' costumes = Fabric used for girls' costumes + 6 meters (2 additional costumes * 3 meters per costume)

Using the given information, we can set up the equation as follows:

54 meters = 48 meters + 6 meters

Simplifying the equation, we find:

54 meters = 54 meters

This equation is true, which means our assumption that the number of costumes sewn for girls is x is correct.

Therefore, the number of costumes sewn for boys is x + 2.

To find the value of x, we can solve the equation:

48 meters = x * 3 meters (fabric used for each girl's costume)

Simplifying the equation, we find:

x = 48 meters / 3 meters

x = 16

Therefore, the number of costumes sewn for girls is 16, and the number of costumes sewn for boys is 16 + 2 = 18.

Answer

The workshop sewed 18 costumes for boys and 16 costumes for girls.