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egoroff_w [7]
3 years ago
8

Una fábrica produce tres tipos de balones de fútbol, con un costo mensual de

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
5 0

Answer:

Se fabricaron:

1000 balones de los que cuestan $20

75 balones de los que cuestan $30

50 balones de los que cuestan $40

Step-by-step explanation:

Vamos a definir las variables:

x = número de balones de $100.00 vendidos.

y = número de balones de $120.00 vendidos

z = número de balones de $160,00 vendidos.

Sabemos que se producen 1125 balones, entonces:

x + y + z = 1125

y el costo de producción es $24,250, conociendo el costo de cada balón podemos escribir:

x*$20 + y*$30 + z*$40 = $24,250

Y también sabemos que la ganancia mensual es $92,750

Ganancia es la diferencia entre el dinero total recibido y los costos, entonces:

x*$100 + y*$120 + z*$160 - $24,250 =  $92,750

x*$100 + y*$120 + z*$160 = $92,750 + $24,250

x*$100 + y*$120 + z*$160 = $117,000

Entonces tenemos un sistema de 3 ecuaciones:

x + y + z = 1125

x*$20 + y*$30 + z*$40 = $24,250

x*$100 + y*$120 + z*$160 = $117,000

Para resolver esto debemos comenzar por aislar alguna variable en alguna de las ecuaciones, yo comenzare aislando x en la primera ecuación:

x = 1125 - y - z

Ahora podemos reemplazar esto en las otras dos ecuaciones para obtener:

(1125 - y - z)*$20 + y*$30 + z*$40 = $24,250

(1125 - y - z)*$100 + y*$120 + z*$160 = $117,000

Si simplificamos esto obtenemos:

$22,500 + y*$10 + z*$20 = $24,250

$112,500 + y*$20 + z*$60 =  $117,000

Ahora de vuelta, debemos aislar una variable en una de las ecuaciones, si aislamos y en la primera ecuación obtenemos:

y*$10 = $24,250 - $22,500 -  z*$20

y = ($1,750 - z*$20)/$10

y = 175 - 2*z

Reemplazando esto en la otra ecuación obtenemos:

$112,500 + (175 - 2*z)*$20 + z*$60 =  $117,000

Ahora podemos resolver esto para z.

(175 - 2*z)*$20 + z*$60 =  $117,000 - $112,500

(175 - 2*z)*$20 + z*$60 = $4,500

$3,500 - z*$40 + z*$60 = $4,500

$3,500 + z*$20 = $4,500

z*$20 = $4,500 - $3,500 = $1,000

z = $1,000/$20 = 50

Entonces tenemos 50 balones de los que cuestan $40.

Usando la ecuación y = 175 - 2*z podemos encontrar el valor de y.

y = 175 - 2*50 = 75

Entonces tenemos 75 balones de los que cuestan $30.

Usando la ecuación x = 1125 - y - z podemos encontrar el valor de x.

x = 1125 - 75 - 50 = 1000

tenemos 1000 balones de $20.

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