Question

Una diseñadora de modas que confecciona trajes de noche, tarda 3 horas en cortar y 2 horas en coser cada vestido de fiesta. Para confeccionar un terno tarde 3 horas en cortar y 3 en coser. En una semana de trabajo la diseñadora dispone de 30 horas para corte y 25 horas para el cosido. Hallé el número de trajes de noche de cada tipo que pueden producirse en una semana, teniendo en cuenta que la diseñadora trabaja de aprovechando toda su capacidad

Answer 1

For this case we define the following variables:

x: Number of party dresses

y: Number of suits

You have 30 hours per week to cut, that is, the first equation is given by:

`3x + 3y = 30\\`

It is also known that 25 hours per week are available for sewing, that is:

`2x + 3y = 25\\`

It has a system of two equations with two unknowns, solving we have:

`3x + 3y = 30\\\\2x + 3y = 25\\`

Multiplying the second equation by -1:

`3x + 3y = 30\\\\-2x-3y = -25\\`

Adding up:

`x + 0 = 5\\\\x = 5\\`

Substituting x in the first equation:

`3 * 5 + 3y = 30\\\\15 + 3y = 30\\`

Clearing and:

`3y = 30-15\\\\3y = 15\\`

`y = (15)/(3)\\\\y = 5\\`

Thus, per week, the designer can produce 5 party dresses and 5 suits working at her maximum capacity.

Answer:

5 Party dresses

5 Suits